feat: implement consistent-mass HHT shell dynamics
This commit is contained in:
KOKO\Mimi
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#include "fesa/analysis/dynamic_analysis_state.h"
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#include <gtest/gtest.h>
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#include <array>
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#include <cmath>
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#include <cstdint>
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#include <filesystem>
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#include <functional>
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#include <limits>
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#include <memory>
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#include <optional>
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#include <stdexcept>
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#include <utility>
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#include <vector>
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#include "fesa/analysis/analysis_model.h"
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#include "fesa/fem/dof_manager.h"
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namespace {
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constexpr std::array<std::array<double, 3>, 3> kIdentityTriad{
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std::array<double, 3>{1.0, 0.0, 0.0}, std::array<double, 3>{0.0, 1.0, 0.0},
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std::array<double, 3>{0.0, 0.0, 1.0}};
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fesa::ModelDefinition MakeDefinition(const bool fixed = true) {
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const std::filesystem::path source{"dynamic-state.inp"};
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fesa::ModelDefinition definition{};
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definition.source_path = source;
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definition.source_content_identity = "hht-output-unit-fixture";
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definition.nodes = {{{"Shell-A", 10, "0010"}, {0.0, 0.0, 0.0}, {source, 1U}},
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{{"Shell-A", 20, "20"}, {1.0, 0.0, 0.0}, {source, 2U}},
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{{"Shell-A", 30, "30"}, {1.0, 1.0, 0.0}, {source, 3U}},
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{{"Shell-A", 40, "40"}, {0.0, 1.0, 0.0}, {source, 4U}}};
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definition.materials = {{"Material", 1000.0, 0.25, {source, 5U}}};
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definition.densities = {{0U, 2.0, {source, 6U}}};
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definition.shell_sections = {{"Shell", 0.1, 0U, {source, 7U}}};
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definition.shell_elements = {{{"Shell-A", 9, "0009"},
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fesa::ShellSourceElementType::kS4,
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{0U, 1U, 2U, 3U},
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0U,
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0U,
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{source, 8U}}};
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for (std::size_t node = 0U; node < 4U; ++node) {
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definition.shell_node_initial_frames.push_back(
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{static_cast<fesa::EntityIndex>(node),
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{0.0, 0.0, 1.0},
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{1.0, 0.0, 0.0},
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{0.0, 1.0, 0.0}});
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}
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definition.node_sets = {{"All", std::nullopt, {0U, 1U, 2U, 3U}, {source, 9U}},
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{"Loaded", std::nullopt, {0U}, {source, 10U}}};
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fesa::DynamicStepDefinition step{};
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step.source_step_name_raw = "Transient Load";
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step.source_step_name_canonical = "TRANSIENT LOAD";
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step.initial_increment = 0.25;
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step.time_period = 0.5;
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step.increment_count = 2U;
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step.maximum_increments = 3U;
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if (fixed) {
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step.boundaries = {{"All", 1, 6, 0.0, {source, 11U}}};
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step.loads = {{"Loaded", 3, 4.0, {source, 12U}}};
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}
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definition.dynamic_step = step;
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return definition;
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}
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struct Fixture {
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std::unique_ptr<fesa::Domain> domain;
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fesa::DynamicAnalysisState state;
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};
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Fixture MakeFixture(fesa::ModelDefinition definition = MakeDefinition()) {
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auto domain_result = fesa::Domain::Create(std::move(definition));
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if (!domain_result.HasValue())
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throw std::runtime_error{"Invalid fixture Domain."};
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auto domain =
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std::make_unique<fesa::Domain>(std::move(domain_result.Value()));
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auto model = fesa::AnalysisModel::Create(*domain);
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if (!model.HasValue())
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throw std::runtime_error{"Invalid fixture AnalysisModel."};
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auto dofs = fesa::DofManager::Create(model.Value());
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if (!dofs.HasValue()) throw std::runtime_error{"Invalid fixture DofManager."};
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auto state = fesa::DynamicAnalysisState::Create(*domain, dofs.Value());
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if (!state.HasValue()) throw std::runtime_error{"Invalid fixture state."};
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return {std::move(domain), std::move(state.Value())};
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}
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// A fully restrained, initially undeformed shell under a dead nodal force has
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// zero motion and strain, and nonzero support force at every accepted endpoint.
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fesa::DynamicAcceptedFrameState MakeFrame(const fesa::Domain& domain,
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const std::uint32_t index) {
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fesa::DynamicAcceptedFrameState frame{};
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frame.frame_index = index;
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frame.increment_index = index;
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frame.time = static_cast<double>(index) * domain.Dynamic()->initial_increment;
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frame.is_initial = index == 0U;
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for (std::size_t node = 0U; node < domain.Nodes().size(); ++node) {
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frame.nodal_internal_order.push_back(static_cast<fesa::EntityIndex>(node));
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frame.nodal_source_ids.push_back(domain.Nodes()[node].source_id);
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frame.nodal_triad.push_back(kIdentityTriad);
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frame.nodal_director.push_back({0.0, 0.0, 1.0});
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}
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for (auto* vector :
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{&frame.generalized_coordinates, &frame.velocity, &frame.acceleration,
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&frame.algorithmic_acceleration, &frame.inertia_force,
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&frame.internal_force, &frame.external_force, &frame.residual,
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&frame.reaction, &frame.residual_scale}) {
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*vector = fesa::Vector{24U};
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}
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frame.angular_velocity = fesa::Vector{12U};
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frame.angular_acceleration = fesa::Vector{12U};
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if (!domain.Dynamic()->loads.empty()) {
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frame.external_force[2U] = 4.0;
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frame.residual[2U] = -4.0;
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frame.reaction[2U] = -4.0;
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frame.residual_scale[2U] = 4.0;
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}
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const double gauss = 1.0 / std::sqrt(3.0);
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const std::array<std::array<double, 2>, 4> natural{
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std::array<double, 2>{-gauss, -gauss},
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{gauss, -gauss},
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{gauss, gauss},
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{-gauss, gauss}};
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const std::array<fesa::ShellMidsurfaceLocation, 4> locations{
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fesa::ShellMidsurfaceLocation::kGp1, fesa::ShellMidsurfaceLocation::kGp2,
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fesa::ShellMidsurfaceLocation::kGp3, fesa::ShellMidsurfaceLocation::kGp4};
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for (std::size_t point = 0U; point < 4U; ++point) {
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frame.shell_results.push_back(
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{0U,
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locations[point],
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natural[point],
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kIdentityTriad,
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{},
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{},
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{{{fesa::ShellSectionPosition::kBottom, -1.0, {}},
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{fesa::ShellSectionPosition::kMiddle, 0.0, {}},
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{fesa::ShellSectionPosition::kTop, 1.0, {}}}}});
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}
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return frame;
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}
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TEST(DynamicAnalysisState, DefaultStateRejectsTrialAndCommit) {
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fesa::DynamicAnalysisState state;
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EXPECT_FALSE(state.IsInitialized());
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EXPECT_TRUE(state.AcceptedFrames().empty());
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EXPECT_FALSE(state.BeginTrialFromCommitted().HasValue());
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EXPECT_THROW((void)state.CommittedState(), std::logic_error);
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const auto status = state.CommitAcceptedFrame({});
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EXPECT_FALSE(status.IsOk());
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ASSERT_EQ(status.Diagnostics().size(), 1U);
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EXPECT_EQ(status.Diagnostics()[0U].code, "dynamic-invalid-state");
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}
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TEST(DynamicAnalysisState,
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CommitsCompleteZeroCorrectionHistoryAndCopiesTrials) {
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auto fixture = MakeFixture();
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EXPECT_TRUE(fixture.state.IsInitialized());
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EXPECT_FALSE(fixture.state.BeginTrialFromCommitted().HasValue());
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for (std::uint32_t index = 0U; index <= 2U; ++index) {
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auto frame = MakeFrame(*fixture.domain, index);
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ASSERT_TRUE(fixture.state.CommitAcceptedFrame(frame).IsOk());
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frame.reaction[2U] = 123.0;
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EXPECT_DOUBLE_EQ(fixture.state.CommittedState().reaction[2U], -4.0);
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EXPECT_EQ(fixture.state.AcceptedFrames().size(), index + 1U);
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}
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auto trial = fixture.state.BeginTrialFromCommitted();
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ASSERT_TRUE(trial.HasValue());
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trial.Value().generalized_coordinates[0U] = 1.0;
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trial.Value().shell_results[0U].stress[0U].components[0U] = 1.0;
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fixture.state.DiscardTrial();
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EXPECT_DOUBLE_EQ(fixture.state.CommittedState().generalized_coordinates[0U],
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0.0);
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EXPECT_DOUBLE_EQ(fixture.state.CommittedState()
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.shell_results[0U]
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.stress[0U]
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.components[0U],
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0.0);
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EXPECT_DOUBLE_EQ(fixture.state.CommittedState().time, 0.5);
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EXPECT_FALSE(
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fixture.state.CommitAcceptedFrame(MakeFrame(*fixture.domain, 3U)).IsOk());
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EXPECT_EQ(fixture.state.AcceptedFrames().size(), 3U);
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}
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TEST(DynamicAnalysisState,
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RejectsMalformedInventoryScheduleAndPreservesEndpoint) {
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auto fixture = MakeFixture();
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ASSERT_TRUE(
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fixture.state.CommitAcceptedFrame(MakeFrame(*fixture.domain, 0U)).IsOk());
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using Frame = fesa::DynamicAcceptedFrameState;
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const std::vector<std::function<void(Frame&)>> mutations{
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[](Frame& frame) { frame.frame_index = 2U; },
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[](Frame& frame) { frame.increment_index = 2U; },
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[](Frame& frame) { frame.time = 0.26; },
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[](Frame& frame) {
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frame.time = std::numeric_limits<double>::quiet_NaN();
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},
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[](Frame& frame) { frame.is_initial = true; },
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[](Frame& frame) { frame.iteration_count = 101U; },
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[](Frame& frame) { frame.nodal_internal_order[1U] = 0U; },
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[](Frame& frame) {
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frame.nodal_source_ids[1U].source_label_text = "wrong";
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},
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[](Frame& frame) { frame.nodal_triad.pop_back(); },
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[](Frame& frame) {
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frame.nodal_director[0U][2U] = std::numeric_limits<double>::infinity();
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},
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[](Frame& frame) { frame.acceleration = fesa::Vector{23U}; },
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[](Frame& frame) { frame.velocity[0U] = 1.0; },
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[](Frame& frame) { frame.acceleration[0U] = 1.0; },
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[](Frame& frame) { frame.algorithmic_acceleration[0U] = 1.0; },
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[](Frame& frame) { frame.generalized_coordinates[0U] = 1.0; },
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[](Frame& frame) { frame.reaction[2U] = 0.0; },
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[](Frame& frame) { frame.residual[2U] = 0.0; },
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[](Frame& frame) { frame.residual_scale[0U] = -1.0; },
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[](Frame& frame) {
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frame.external_force[0U] = 1.0;
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frame.residual[0U] = -1.0;
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frame.reaction[0U] = -1.0;
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},
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[](Frame& frame) { frame.shell_results.pop_back(); },
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[](Frame& frame) { frame.shell_results[0U].element = 1U; },
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[](Frame& frame) {
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frame.shell_results[0U].natural_coordinates[0U] = 0.0;
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},
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[](Frame& frame) { frame.shell_results[0U].stress[0U].zeta = 0.0; },
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[](Frame& frame) {
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frame.shell_results[0U].stress[0U].components[0U] =
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std::numeric_limits<double>::quiet_NaN();
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},
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[](Frame& frame) {
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frame.kinetic_energy = std::numeric_limits<double>::infinity();
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},
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[](Frame& frame) {
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frame.angular_momentum_rate[0U] =
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std::numeric_limits<double>::quiet_NaN();
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},
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[](Frame& frame) { frame.hidden_constraint = fesa::Vector{1U}; },
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[](Frame& frame) { frame.free_residual_metrics[0U] = -1.0; }};
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for (std::size_t index = 0U; index < mutations.size(); ++index) {
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SCOPED_TRACE(index);
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auto frame = MakeFrame(*fixture.domain, 1U);
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mutations[index](frame);
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const auto status = fixture.state.CommitAcceptedFrame(frame);
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ASSERT_FALSE(status.IsOk());
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ASSERT_EQ(status.Diagnostics().size(), 1U);
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EXPECT_EQ(status.Diagnostics()[0U].code, "dynamic-invalid-state");
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ASSERT_EQ(fixture.state.AcceptedFrames().size(), 1U);
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EXPECT_DOUBLE_EQ(fixture.state.CommittedState().time, 0.0);
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EXPECT_DOUBLE_EQ(fixture.state.CommittedState().reaction[2U], -4.0);
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}
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EXPECT_TRUE(
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fixture.state.CommitAcceptedFrame(MakeFrame(*fixture.domain, 1U)).IsOk());
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}
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TEST(DynamicAnalysisState, RejectsInvalidInitialStateAndFreeReaction) {
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auto fixture = MakeFixture(MakeDefinition(false));
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auto initial = MakeFrame(*fixture.domain, 0U);
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initial.generalized_coordinates[0U] = 1.0;
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EXPECT_FALSE(fixture.state.CommitAcceptedFrame(initial).IsOk());
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initial = MakeFrame(*fixture.domain, 0U);
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initial.acceleration[0U] = 1.0;
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EXPECT_FALSE(fixture.state.CommitAcceptedFrame(initial).IsOk());
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initial = MakeFrame(*fixture.domain, 0U);
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initial.time = -0.0;
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EXPECT_FALSE(fixture.state.CommitAcceptedFrame(initial).IsOk());
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initial = MakeFrame(*fixture.domain, 0U);
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initial.reaction[0U] = 1.0;
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EXPECT_FALSE(fixture.state.CommitAcceptedFrame(initial).IsOk());
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EXPECT_TRUE(fixture.state.AcceptedFrames().empty());
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EXPECT_TRUE(
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fixture.state.CommitAcceptedFrame(MakeFrame(*fixture.domain, 0U)).IsOk());
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}
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TEST(DynamicAnalysisState, CreateRejectsInvalidScheduleAndNonzeroBoundary) {
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const std::vector<std::function<void(fesa::ModelDefinition&)>> mutations{
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[](auto& definition) { definition.dynamic_step->increment_count = 0U; },
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[](auto& definition) { definition.dynamic_step->time_period = 0.6; },
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[](auto& definition) {
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definition.dynamic_step->maximum_increments = 1U;
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},
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[](auto& definition) {
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definition.dynamic_step->initial_increment =
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std::numeric_limits<double>::quiet_NaN();
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},
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[](auto& definition) {
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definition.dynamic_step->boundaries[0U].value = 1.0;
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}};
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for (std::size_t index = 0U; index < mutations.size(); ++index) {
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SCOPED_TRACE(index);
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auto definition = MakeDefinition();
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mutations[index](definition);
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auto domain = fesa::Domain::Create(std::move(definition));
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ASSERT_TRUE(domain.HasValue());
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auto model = fesa::AnalysisModel::Create(domain.Value());
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ASSERT_TRUE(model.HasValue());
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auto dofs = fesa::DofManager::Create(model.Value());
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ASSERT_TRUE(dofs.HasValue());
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EXPECT_FALSE(
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fesa::DynamicAnalysisState::Create(domain.Value(), dofs.Value())
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.HasValue());
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}
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}
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} // namespace
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@@ -0,0 +1,330 @@
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#include <gtest/gtest.h>
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#include <array>
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#include <cmath>
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#include <cstddef>
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#include <memory>
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#include <optional>
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#include <stdexcept>
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#include <utility>
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#include <vector>
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#include "analysis/hht_dynamic_internal.h"
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#include "fesa/analysis/analysis_model.h"
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#include "fesa/math/matrix.h"
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#include "fesa/solvers/linear/mkl_pardiso_solver.h"
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#include "fesa/solvers/linear/mkl_pardiso_tangent_solver.h"
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namespace {
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struct Fixture {
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std::unique_ptr<fesa::Domain> domain;
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fesa::DofManager dofs;
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};
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Fixture MakeFixture(const std::size_t free_nodes = 1U,
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const bool partial_rotation = false,
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const bool translations_free = true) {
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fesa::ModelDefinition definition{};
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definition.source_path = "hht-algebra.inp";
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definition.nodes = {
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{{"Plate", 1, "1"}, {-1, -1, 0}, {definition.source_path, 1U}},
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{{"Plate", 2, "2"}, {1, -1, 0}, {definition.source_path, 2U}},
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{{"Plate", 3, "3"}, {1, 1, 0}, {definition.source_path, 3U}},
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{{"Plate", 4, "4"}, {-1, 1, 0}, {definition.source_path, 4U}}};
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definition.materials = {{"Elastic", 1000, 0.3, {definition.source_path, 5U}}};
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definition.densities = {{0U, 1.0, {definition.source_path, 6U}}};
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definition.shell_sections = {
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{"Plate", 0.2, 0U, {definition.source_path, 7U}}};
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definition.shell_elements = {{{"Plate", 1, "1"},
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fesa::ShellSourceElementType::kS4,
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{0U, 1U, 2U, 3U},
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0U,
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0U,
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{definition.source_path, 8U}}};
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fesa::DynamicStepDefinition step{};
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step.source_step_name_raw = "Dynamic";
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step.source_step_name_canonical = "DYNAMIC";
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step.initial_increment = 0.1;
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step.time_period = 0.1;
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step.increment_count = 1U;
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step.maximum_increments = 1U;
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for (std::size_t i = 0; i < 4; ++i) {
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definition.shell_node_initial_frames.push_back(
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{static_cast<fesa::EntityIndex>(i), {0, 0, 1}, {1, 0, 0}, {0, 1, 0}});
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const std::string name = "Node" + std::to_string(i);
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definition.node_sets.push_back({name,
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std::nullopt,
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{static_cast<fesa::EntityIndex>(i)},
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{definition.source_path, 9U}});
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if (i >= free_nodes) {
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step.boundaries.push_back(
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{name, 1, 6, 0.0, {definition.source_path, 10U}});
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} else {
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if (partial_rotation)
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step.boundaries.push_back(
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{name, 4, 5, 0.0, {definition.source_path, 10U}});
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if (!translations_free)
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step.boundaries.push_back(
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{name, 1, 3, 0.0, {definition.source_path, 10U}});
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}
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}
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definition.dynamic_step = step;
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auto result = fesa::Domain::Create(std::move(definition));
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if (!result.HasValue()) throw std::runtime_error{"Invalid algebra domain."};
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auto domain = std::make_unique<fesa::Domain>(std::move(result.Value()));
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auto model = fesa::AnalysisModel::Create(*domain);
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if (!model.HasValue()) throw std::runtime_error{"Invalid algebra model."};
|
||||
auto dofs = fesa::DofManager::Create(model.Value());
|
||||
if (!dofs.HasValue()) throw std::runtime_error{"Invalid algebra DOFs."};
|
||||
return {std::move(domain), std::move(dofs.Value())};
|
||||
}
|
||||
|
||||
fesa::SparseMatrix Sparse(const fesa::Matrix& matrix) {
|
||||
std::vector<fesa::CooContribution> entries;
|
||||
for (std::size_t i = 0; i < matrix.Rows(); ++i) {
|
||||
for (std::size_t j = 0; j < matrix.Columns(); ++j) {
|
||||
entries.push_back({i, j, matrix(i, j), 0U, entries.size()});
|
||||
}
|
||||
}
|
||||
auto result = fesa::hht_internal::MakeSparse(matrix.Rows(), matrix.Columns(),
|
||||
std::move(entries));
|
||||
EXPECT_TRUE(result.HasValue());
|
||||
return std::move(result.Value());
|
||||
}
|
||||
|
||||
fesa::hht_internal::DynamicAssembly Assembly(
|
||||
const double second_stiffness = 3.0, const double mass_scale = 1.0) {
|
||||
fesa::DynamicAcceptedFrameState frame;
|
||||
frame.is_initial = true;
|
||||
for (auto* vector :
|
||||
{&frame.generalized_coordinates, &frame.velocity, &frame.acceleration,
|
||||
&frame.algorithmic_acceleration, &frame.inertia_force,
|
||||
&frame.internal_force, &frame.external_force, &frame.residual,
|
||||
&frame.residual_scale})
|
||||
*vector = fesa::Vector{24U};
|
||||
frame.external_force[0] = 2.0;
|
||||
frame.residual_scale[0] = 2.0;
|
||||
fesa::Matrix mass{24U, 24U};
|
||||
fesa::Matrix stiffness{24U, 24U};
|
||||
fesa::Matrix metric{24U, 24U};
|
||||
std::vector<fesa::DynamicRotationKinematics> rotations;
|
||||
for (std::size_t i = 0; i < 4; ++i) {
|
||||
const std::size_t base = 6U * i;
|
||||
for (std::size_t j = 0; j < 5; ++j)
|
||||
mass(base + j, base + j) = mass_scale * (j < 3U ? 2.0 : 1.0);
|
||||
const double k = i == 1U ? second_stiffness : 3.0;
|
||||
stiffness(base, base) = 8.0 + k * 0.7 * 0.7;
|
||||
stiffness(base, base + 5U) = -0.7 * k;
|
||||
stiffness(base + 5U, base) = -0.7 * k;
|
||||
stiffness(base + 5U, base + 5U) = k;
|
||||
metric(base + 5U, base + 5U) = 3.0;
|
||||
auto rotation = fesa::EvaluateDynamicRotation({}, {0, 0, 1}, {}, {});
|
||||
EXPECT_TRUE(rotation.HasValue());
|
||||
rotations.push_back(std::move(rotation.Value()));
|
||||
}
|
||||
return {std::move(frame),
|
||||
Sparse(mass),
|
||||
Sparse(stiffness),
|
||||
Sparse(stiffness),
|
||||
Sparse(metric),
|
||||
fesa::Vector{24U},
|
||||
fesa::Vector{24U},
|
||||
std::move(rotations),
|
||||
0.0,
|
||||
0.0,
|
||||
fesa::Vector{4U},
|
||||
fesa::Vector{4U}};
|
||||
}
|
||||
|
||||
TEST(HhtDynamicAlgebra,
|
||||
InitializesCoupledMasslessAccelerationFromHiddenEquation) {
|
||||
const auto fixture = MakeFixture();
|
||||
auto assembly = Assembly();
|
||||
fesa::MklPardisoSolver positive;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
const auto acceleration = fesa::hht_internal::InitializeAcceleration(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, positive, tangent);
|
||||
ASSERT_TRUE(acceleration.HasValue());
|
||||
EXPECT_NEAR(acceleration.Value()[0], 1.0, 1.0e-12);
|
||||
EXPECT_NEAR(acceleration.Value()[5], 0.7, 1.0e-12);
|
||||
for (const auto full : fixture.dofs.ConstrainedDofs())
|
||||
EXPECT_EQ(acceleration.Value()[full], 0.0);
|
||||
const auto nodes =
|
||||
fesa::hht_internal::NullNodes(fixture.dofs, assembly.rotations);
|
||||
ASSERT_EQ(nodes, std::vector<std::size_t>{0U});
|
||||
assembly.frame.acceleration = acceleration.Value();
|
||||
auto frame = assembly.frame;
|
||||
EXPECT_TRUE(fesa::hht_internal::CompleteConstraintEvidence(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, nodes, positive,
|
||||
tangent, &frame)
|
||||
.IsOk());
|
||||
ASSERT_EQ(frame.hidden_acceleration_defect.Size(), 1U);
|
||||
EXPECT_NEAR(frame.hidden_acceleration_defect[0], 0.0, 1.0e-12);
|
||||
EXPECT_GT(frame.hidden_acceleration_defect_scale[0], 0.0);
|
||||
frame.acceleration[5] = 0.0;
|
||||
const auto pseudoinverse = fesa::hht_internal::CompleteConstraintEvidence(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, nodes, positive, tangent,
|
||||
&frame);
|
||||
EXPECT_FALSE(pseudoinverse.IsOk());
|
||||
}
|
||||
|
||||
TEST(HhtDynamicAlgebra, ChecksInitialConstraintAndVelocityWithoutRepair) {
|
||||
const auto fixture = MakeFixture();
|
||||
fesa::MklPardisoSolver positive;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
auto inconsistent = Assembly();
|
||||
inconsistent.frame.internal_force[5] = 0.3;
|
||||
inconsistent.frame.residual_scale[5] = 0.3;
|
||||
EXPECT_FALSE(
|
||||
fesa::hht_internal::InitializeAcceleration(
|
||||
*fixture.domain, fixture.dofs, inconsistent, 2.0, positive, tangent)
|
||||
.HasValue());
|
||||
inconsistent = Assembly();
|
||||
inconsistent.frame.velocity[5] = 0.1;
|
||||
EXPECT_FALSE(
|
||||
fesa::hht_internal::InitializeAcceleration(
|
||||
*fixture.domain, fixture.dofs, inconsistent, 2.0, positive, tangent)
|
||||
.HasValue());
|
||||
}
|
||||
|
||||
TEST(HhtDynamicAlgebra, KeepsAcceptedHiddenRateDefectsAsDiagnostics) {
|
||||
const auto fixture = MakeFixture();
|
||||
auto assembly = Assembly();
|
||||
assembly.frame.is_initial = false;
|
||||
assembly.frame.velocity[5] = 0.1;
|
||||
assembly.frame.acceleration[5] = -0.2;
|
||||
auto frame = assembly.frame;
|
||||
fesa::MklPardisoSolver positive;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
const auto nodes =
|
||||
fesa::hht_internal::NullNodes(fixture.dofs, assembly.rotations);
|
||||
const auto result = fesa::hht_internal::CompleteConstraintEvidence(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, nodes, positive, tangent,
|
||||
&frame);
|
||||
ASSERT_TRUE(result.IsOk());
|
||||
EXPECT_NEAR(frame.hidden_velocity_defect[0], 0.3, 1.0e-12);
|
||||
EXPECT_NEAR(frame.hidden_acceleration_defect[0], -0.6, 1.0e-12);
|
||||
}
|
||||
|
||||
TEST(HhtDynamicAlgebra, RejectsNegativePhysicalMassAndAlgebraicRankLoss) {
|
||||
const auto fixture = MakeFixture(2U);
|
||||
fesa::MklPardisoSolver positive;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
const auto negative = Assembly(3.0, -1.0);
|
||||
EXPECT_FALSE(
|
||||
fesa::hht_internal::InitializeAcceleration(
|
||||
*fixture.domain, fixture.dofs, negative, 2.0, positive, tangent)
|
||||
.HasValue());
|
||||
const auto singular = Assembly(0.0);
|
||||
EXPECT_FALSE(
|
||||
fesa::hht_internal::InitializeAcceleration(
|
||||
*fixture.domain, fixture.dofs, singular, 2.0, positive, tangent)
|
||||
.HasValue());
|
||||
}
|
||||
|
||||
TEST(HhtDynamicAlgebra, AppliesTheExactRegularityConditionBoundary) {
|
||||
const auto fixture = MakeFixture(2U);
|
||||
fesa::MklPardisoSolver positive;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
for (const int exponent : {31, 32, 33}) {
|
||||
auto assembly = Assembly();
|
||||
// The boundary oracle is exactly diag(1,c), with W=I. Avoid a rounded
|
||||
// sqrt(3) congruence when testing a binary-exact inclusive threshold.
|
||||
fesa::Matrix stiffness{24U, 24U};
|
||||
fesa::Matrix metric{24U, 24U};
|
||||
for (std::size_t node = 0; node < 4; ++node) {
|
||||
const std::size_t drill = 6U * node + 5U;
|
||||
stiffness(drill, drill) = node == 1U ? std::ldexp(1.0, -exponent) : 1.0;
|
||||
metric(drill, drill) = 1.0;
|
||||
}
|
||||
assembly.internal_tangent = Sparse(stiffness);
|
||||
assembly.drilling_metric = Sparse(metric);
|
||||
const auto result = fesa::hht_internal::InitializeAcceleration(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, positive, tangent);
|
||||
EXPECT_EQ(result.HasValue(), exponent <= 32)
|
||||
<< exponent
|
||||
<< (result.HasValue() ? ""
|
||||
: result.GetStatus().Diagnostics()[0].message);
|
||||
if (exponent == 33) {
|
||||
ASSERT_FALSE(result.HasValue());
|
||||
EXPECT_EQ(result.GetStatus().Diagnostics()[0].code,
|
||||
"dynamic-algebraic-conditioning");
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
TEST(HhtDynamicAlgebra, AllFixedModelHasAnEmptyValidAccelerationSolve) {
|
||||
const auto fixture = MakeFixture(0U);
|
||||
auto assembly = Assembly();
|
||||
fesa::MklPardisoSolver positive;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
const auto result = fesa::hht_internal::InitializeAcceleration(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, positive, tangent);
|
||||
ASSERT_TRUE(result.HasValue());
|
||||
EXPECT_EQ(result.Value().Norm(), 0.0);
|
||||
auto frame = assembly.frame;
|
||||
EXPECT_TRUE(fesa::hht_internal::CompleteConstraintEvidence(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, {}, positive,
|
||||
tangent, &frame)
|
||||
.IsOk());
|
||||
EXPECT_EQ(frame.hidden_constraint.Size(), 0U);
|
||||
}
|
||||
|
||||
TEST(HhtDynamicAlgebra, PartialBoundaryRetainsEveryNonzeroPhysicalDirection) {
|
||||
for (const bool translations_free : {false, true}) {
|
||||
const auto fixture = MakeFixture(1U, true, translations_free);
|
||||
for (const double p : {0.0, 1.0 / 2000.0, 1.0e-8}) {
|
||||
auto assembly = Assembly();
|
||||
assembly.frame.external_force[0] = 0.0;
|
||||
fesa::Matrix mass{24U, 24U};
|
||||
const double nz = std::sqrt(1.0 - p * p);
|
||||
for (std::size_t node = 0; node < 4; ++node) {
|
||||
for (std::size_t j = 0; j < 3; ++j)
|
||||
mass(6U * node + j, 6U * node + j) = 2.0;
|
||||
mass(6U * node + 3U, 6U * node + 3U) = nz * nz;
|
||||
mass(6U * node + 4U, 6U * node + 4U) = 1.0;
|
||||
mass(6U * node + 5U, 6U * node + 5U) = p * p;
|
||||
mass(6U * node + 3U, 6U * node + 5U) = -p * nz;
|
||||
mass(6U * node + 5U, 6U * node + 3U) = -p * nz;
|
||||
assembly.rotations[node].drill_null = {p, 0, nz};
|
||||
}
|
||||
assembly.mass = Sparse(mass);
|
||||
const auto nodes =
|
||||
fesa::hht_internal::NullNodes(fixture.dofs, assembly.rotations);
|
||||
EXPECT_EQ(nodes.size(), p == 0.0 ? 1U : 0U);
|
||||
fesa::MklPardisoSolver positive;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
const auto result = fesa::hht_internal::InitializeAcceleration(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, positive, tangent);
|
||||
const bool expected = !(translations_free && p == 1.0e-8);
|
||||
EXPECT_EQ(result.HasValue(), expected) << "p=" << p;
|
||||
if (!expected) {
|
||||
ASSERT_FALSE(result.HasValue());
|
||||
EXPECT_EQ(result.GetStatus().Diagnostics()[0].code,
|
||||
"dynamic-positive-mass-conditioning");
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
TEST(HhtDynamicAlgebra, RejectsAdmissibleNullRankChangeBeforeAcceptingFrame) {
|
||||
const auto fixture = MakeFixture(1U, true);
|
||||
auto assembly = Assembly();
|
||||
const auto initial_nodes =
|
||||
fesa::hht_internal::NullNodes(fixture.dofs, assembly.rotations);
|
||||
ASSERT_EQ(initial_nodes.size(), 1U);
|
||||
assembly.rotations[0].drill_null = {1.0e-8, 0, std::sqrt(1.0 - 1.0e-16)};
|
||||
auto frame = assembly.frame;
|
||||
frame.hidden_constraint = fesa::Vector{1U, 23.0};
|
||||
fesa::MklPardisoSolver positive;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
const auto result = fesa::hht_internal::CompleteConstraintEvidence(
|
||||
*fixture.domain, fixture.dofs, assembly, 2.0, initial_nodes, positive,
|
||||
tangent, &frame);
|
||||
ASSERT_FALSE(result.IsOk());
|
||||
EXPECT_EQ(result.Diagnostics()[0].code, "dynamic-mass-null-rank-change");
|
||||
EXPECT_EQ(frame.hidden_constraint[0], 23.0);
|
||||
}
|
||||
|
||||
} // namespace
|
||||
@@ -0,0 +1,125 @@
|
||||
#include "fesa/analysis/hht_dynamic_procedure.h"
|
||||
|
||||
#include <gtest/gtest.h>
|
||||
|
||||
#include <filesystem>
|
||||
#include <optional>
|
||||
|
||||
#include "fesa/analysis/newton_iteration_log.h"
|
||||
#include "fesa/assembly/parallel_for.h"
|
||||
#include "fesa/solvers/linear/mkl_pardiso_solver.h"
|
||||
#include "fesa/solvers/linear/mkl_pardiso_tangent_solver.h"
|
||||
namespace {
|
||||
fesa::ModelDefinition MakeDefinition(const bool fixed = true) {
|
||||
const std::filesystem::path source{"dynamic-state.inp"};
|
||||
fesa::ModelDefinition definition{};
|
||||
definition.source_path = source;
|
||||
definition.source_content_identity = "hht-output-unit-fixture";
|
||||
definition.nodes = {{{"Shell-A", 10, "0010"}, {0.0, 0.0, 0.0}, {source, 1U}},
|
||||
{{"Shell-A", 20, "20"}, {1.0, 0.0, 0.0}, {source, 2U}},
|
||||
{{"Shell-A", 30, "30"}, {1.0, 1.0, 0.0}, {source, 3U}},
|
||||
{{"Shell-A", 40, "40"}, {0.0, 1.0, 0.0}, {source, 4U}}};
|
||||
definition.materials = {{"Material", 1000.0, 0.25, {source, 5U}}};
|
||||
definition.densities = {{0U, 2.0, {source, 6U}}};
|
||||
definition.shell_sections = {{"Shell", 0.1, 0U, {source, 7U}}};
|
||||
definition.shell_elements = {{{"Shell-A", 9, "0009"},
|
||||
fesa::ShellSourceElementType::kS4,
|
||||
{0U, 1U, 2U, 3U},
|
||||
0U,
|
||||
0U,
|
||||
{source, 8U}}};
|
||||
for (std::size_t node = 0U; node < 4U; ++node) {
|
||||
definition.shell_node_initial_frames.push_back(
|
||||
{static_cast<fesa::EntityIndex>(node),
|
||||
{0.0, 0.0, 1.0},
|
||||
{1.0, 0.0, 0.0},
|
||||
{0.0, 1.0, 0.0}});
|
||||
}
|
||||
definition.node_sets = {{"All", std::nullopt, {0U, 1U, 2U, 3U}, {source, 9U}},
|
||||
{"Loaded", std::nullopt, {0U}, {source, 10U}}};
|
||||
fesa::DynamicStepDefinition step{};
|
||||
step.source_step_name_raw = "Transient Load";
|
||||
step.source_step_name_canonical = "TRANSIENT LOAD";
|
||||
step.initial_increment = 0.25;
|
||||
step.time_period = 0.5;
|
||||
step.increment_count = 2U;
|
||||
step.maximum_increments = 3U;
|
||||
if (fixed) {
|
||||
step.boundaries = {{"All", 1, 6, 0.0, {source, 11U}}};
|
||||
step.loads = {{"Loaded", 3, 4.0, {source, 12U}}};
|
||||
}
|
||||
definition.dynamic_step = step;
|
||||
return definition;
|
||||
}
|
||||
|
||||
TEST(HhtDynamicProcedure, ClampedStepLoadHasPhysicalReactionAndZeroMotion) {
|
||||
auto domain = fesa::Domain::Create(MakeDefinition());
|
||||
ASSERT_TRUE(domain.HasValue());
|
||||
fesa::SerialParallelFor parallel;
|
||||
fesa::MklPardisoSolver mass;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
fesa::NewtonIterationLogWriter log;
|
||||
const auto path =
|
||||
std::filesystem::temp_directory_path() / "fesa-hht-clamped.log";
|
||||
ASSERT_TRUE(log.Open(path).IsOk());
|
||||
const fesa::HhtDynamicProcedureExecutor executor(parallel, mass, tangent);
|
||||
auto result = executor.Execute(domain.Value(), log);
|
||||
ASSERT_TRUE(log.Close().IsOk());
|
||||
std::filesystem::remove(path);
|
||||
ASSERT_TRUE(result.HasValue())
|
||||
<< (result.HasValue() ? ""
|
||||
: result.GetStatus().Diagnostics().front().message);
|
||||
ASSERT_EQ(result.Value().state.AcceptedFrames().size(), 3U);
|
||||
for (const auto& frame : result.Value().state.AcceptedFrames()) {
|
||||
EXPECT_EQ(frame.iteration_count, 0U);
|
||||
EXPECT_DOUBLE_EQ(frame.reaction[2U], -4.0);
|
||||
EXPECT_DOUBLE_EQ(frame.external_force[2U], 4.0);
|
||||
EXPECT_DOUBLE_EQ(frame.kinetic_energy, 0.0);
|
||||
EXPECT_DOUBLE_EQ(frame.energy_defect, 0.0);
|
||||
for (std::size_t i = 0; i < 24U; ++i) {
|
||||
EXPECT_DOUBLE_EQ(frame.generalized_coordinates[i], 0.0);
|
||||
EXPECT_DOUBLE_EQ(frame.acceleration[i], 0.0);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
TEST(HhtDynamicProcedure, LargeDirectStepStartsFromAcceptedGeometry) {
|
||||
auto definition = MakeDefinition(false);
|
||||
definition.materials[0U].youngs_modulus = 1e9;
|
||||
definition.dynamic_step->increment_count = 1U;
|
||||
definition.dynamic_step->time_period =
|
||||
definition.dynamic_step->initial_increment;
|
||||
definition.node_sets[0U].node_indices = {0U, 3U};
|
||||
definition.node_sets[1U].node_indices = {2U};
|
||||
definition.dynamic_step->boundaries = {
|
||||
{"All", 1, 6, 0.0, {"dynamic-state.inp", 11U}}};
|
||||
definition.dynamic_step->loads = {
|
||||
{"Loaded", 3, -40000.0, {"dynamic-state.inp", 12U}}};
|
||||
auto domain = fesa::Domain::Create(std::move(definition));
|
||||
ASSERT_TRUE(domain.HasValue());
|
||||
fesa::SerialParallelFor parallel;
|
||||
fesa::MklPardisoSolver mass;
|
||||
fesa::MklPardisoTangentSolver tangent;
|
||||
fesa::NewtonIterationLogWriter log;
|
||||
const auto path =
|
||||
std::filesystem::temp_directory_path() / "fesa-hht-large-direct.log";
|
||||
ASSERT_TRUE(log.Open(path).IsOk());
|
||||
auto result = fesa::HhtDynamicProcedureExecutor(parallel, mass, tangent)
|
||||
.Execute(domain.Value(), log);
|
||||
ASSERT_TRUE(log.Close().IsOk());
|
||||
ASSERT_TRUE(result.HasValue())
|
||||
<< (result.HasValue() ? ""
|
||||
: result.GetStatus().Diagnostics().front().message);
|
||||
EXPECT_GT(
|
||||
std::abs(result.Value().state.AcceptedFrames()[0U].acceleration[14U]),
|
||||
1e5);
|
||||
EXPECT_LT(result.Value().state.CommittedState().generalized_coordinates[14U],
|
||||
0.0);
|
||||
for (double metric :
|
||||
result.Value().state.CommittedState().free_residual_metrics)
|
||||
EXPECT_LE(metric, 1e-10);
|
||||
EXPECT_GT(result.Value().state.CommittedState().iteration_count, 0U);
|
||||
std::filesystem::remove(path);
|
||||
}
|
||||
|
||||
} // namespace
|
||||
@@ -0,0 +1,223 @@
|
||||
#include <gtest/gtest.h>
|
||||
|
||||
#include <algorithm>
|
||||
#include <array>
|
||||
#include <cmath>
|
||||
#include <complex>
|
||||
#include <cstddef>
|
||||
#include <iostream>
|
||||
#include <stdexcept>
|
||||
|
||||
#include "fesa/analysis/hht_time_integration.h"
|
||||
|
||||
namespace {
|
||||
|
||||
struct Oscillator {
|
||||
fesa::Vector q{1U};
|
||||
fesa::Vector v{1U};
|
||||
fesa::Vector a{1U};
|
||||
fesa::Vector auxiliary{1U};
|
||||
};
|
||||
|
||||
void Advance(Oscillator* state, const double mass, const double stiffness,
|
||||
const double force, const double h,
|
||||
const fesa::HhtParameters& parameters) {
|
||||
const auto predictor =
|
||||
fesa::PredictHht(state->q, state->v, state->auxiliary, h, parameters);
|
||||
if (!predictor.HasValue())
|
||||
throw std::runtime_error{"Invalid oscillator predictor."};
|
||||
fesa::Vector q{1U};
|
||||
q[0] =
|
||||
(mass * predictor.Value().coordinates[0] +
|
||||
parameters.beta * h * h *
|
||||
((1.0 + parameters.alpha) * force -
|
||||
mass * parameters.alpha * state->a[0])) /
|
||||
(mass + (1.0 + parameters.alpha) * stiffness * parameters.beta * h * h);
|
||||
const auto rates =
|
||||
fesa::EvaluateHhtRates(q, predictor.Value(), state->a, h, parameters);
|
||||
if (!rates.HasValue()) throw std::runtime_error{"Invalid oscillator rates."};
|
||||
state->q = q;
|
||||
state->v = rates.Value().velocity;
|
||||
state->a = rates.Value().acceleration;
|
||||
state->auxiliary = rates.Value().algorithmic_acceleration;
|
||||
}
|
||||
|
||||
using Matrix3 = std::array<std::array<double, 3>, 3>;
|
||||
|
||||
Matrix3 Amplification(const double frequency_step, const double alpha) {
|
||||
// Independent dimensionless recurrence in (q,h*v,h^2*A), with m=1.
|
||||
const double beta = (1.0 - alpha) * (1.0 - alpha) / 4.0;
|
||||
const double gamma = 0.5 - alpha;
|
||||
const double stiffness = frequency_step * frequency_step;
|
||||
Matrix3 matrix{};
|
||||
for (std::size_t column = 0; column < 3; ++column) {
|
||||
const double q = column == 0U ? 1.0 : 0.0;
|
||||
const double velocity = column == 1U ? 1.0 : 0.0;
|
||||
const double auxiliary = column == 2U ? 1.0 : 0.0;
|
||||
const double predictor = q + velocity + (0.5 - beta) * auxiliary;
|
||||
const double next_auxiliary =
|
||||
(-(1.0 + alpha) * stiffness * predictor + alpha * stiffness * q) /
|
||||
(1.0 + (1.0 + alpha) * stiffness * beta);
|
||||
matrix[0][column] = predictor + beta * next_auxiliary;
|
||||
matrix[1][column] =
|
||||
velocity + (1.0 - gamma) * auxiliary + gamma * next_auxiliary;
|
||||
matrix[2][column] = next_auxiliary;
|
||||
}
|
||||
return matrix;
|
||||
}
|
||||
|
||||
std::array<std::complex<double>, 3> Eigenvalues(const Matrix3& matrix) {
|
||||
const double trace = matrix[0][0] + matrix[1][1] + matrix[2][2];
|
||||
const double second =
|
||||
matrix[0][0] * matrix[1][1] + matrix[0][0] * matrix[2][2] +
|
||||
matrix[1][1] * matrix[2][2] - matrix[0][1] * matrix[1][0] -
|
||||
matrix[0][2] * matrix[2][0] - matrix[1][2] * matrix[2][1];
|
||||
const double determinant =
|
||||
matrix[0][0] *
|
||||
(matrix[1][1] * matrix[2][2] - matrix[1][2] * matrix[2][1]) -
|
||||
matrix[0][1] *
|
||||
(matrix[1][0] * matrix[2][2] - matrix[1][2] * matrix[2][0]) +
|
||||
matrix[0][2] *
|
||||
(matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0]);
|
||||
if (determinant == 0.0) {
|
||||
const auto discriminant =
|
||||
std::sqrt(std::complex<double>{trace * trace - 4.0 * second, 0.0});
|
||||
return {std::complex<double>{0.0, 0.0}, 0.5 * (trace + discriminant),
|
||||
0.5 * (trace - discriminant)};
|
||||
}
|
||||
std::array<std::complex<double>, 3> roots{
|
||||
std::complex<double>{1.1, 0.0}, {-0.6, 0.9}, {-0.6, -0.9}};
|
||||
bool converged = false;
|
||||
for (std::size_t iteration = 0; iteration < 500U; ++iteration) {
|
||||
const auto previous = roots;
|
||||
double change = 0.0;
|
||||
for (std::size_t i = 0; i < 3; ++i) {
|
||||
const auto value =
|
||||
((previous[i] - trace) * previous[i] + second) * previous[i] -
|
||||
determinant;
|
||||
const auto denominator = (previous[i] - previous[(i + 1U) % 3U]) *
|
||||
(previous[i] - previous[(i + 2U) % 3U]);
|
||||
roots[i] = previous[i] - value / denominator;
|
||||
change = std::max(change, std::abs(roots[i] - previous[i]));
|
||||
}
|
||||
if (change <= 1.0e-13) {
|
||||
converged = true;
|
||||
break;
|
||||
}
|
||||
}
|
||||
EXPECT_TRUE(converged);
|
||||
for (const auto root : roots) {
|
||||
const double numerator =
|
||||
std::abs(((root - trace) * root + second) * root - determinant);
|
||||
const double scale =
|
||||
std::pow(std::abs(root), 3) + std::abs(trace) * std::norm(root) +
|
||||
std::abs(second) * std::abs(root) + std::abs(determinant);
|
||||
EXPECT_LE(scale > 0.0 ? numerator / scale : numerator, 1.0e-12);
|
||||
}
|
||||
return roots;
|
||||
}
|
||||
|
||||
TEST(HhtEnergyVerification, C07AlphaZeroConservesLinearOscillatorEnergy) {
|
||||
const auto parameters = fesa::MakeHhtParameters(0.0);
|
||||
ASSERT_TRUE(parameters.HasValue());
|
||||
Oscillator state;
|
||||
state.q[0] = 1.0;
|
||||
state.a[0] = -4.0;
|
||||
state.auxiliary = state.a;
|
||||
double maximum = 0.0;
|
||||
for (std::size_t step = 0; step < 640U; ++step) {
|
||||
Advance(&state, 1.0, 4.0, 0.0, 1.0 / 64.0, parameters.Value());
|
||||
const double energy =
|
||||
0.5 * state.v[0] * state.v[0] + 2.0 * state.q[0] * state.q[0];
|
||||
maximum = std::max(maximum, std::abs(energy - 2.0) / 2.0);
|
||||
}
|
||||
std::cout << "C07 alpha0 max energy defect=" << maximum << '\n';
|
||||
EXPECT_LE(maximum, 1.0e-10);
|
||||
}
|
||||
|
||||
TEST(HhtEnergyVerification, C07DefaultAlphaReportsEnergyAndPhaseChanges) {
|
||||
const auto parameters = fesa::MakeHhtParameters(-0.05);
|
||||
ASSERT_TRUE(parameters.HasValue());
|
||||
Oscillator state;
|
||||
state.q[0] = 1.0;
|
||||
state.a[0] = -4.0;
|
||||
state.auxiliary = state.a;
|
||||
double maximum = 0.0;
|
||||
for (std::size_t step = 0; step < 640U; ++step) {
|
||||
Advance(&state, 1.0, 4.0, 0.0, 1.0 / 64.0, parameters.Value());
|
||||
const double energy =
|
||||
0.5 * state.v[0] * state.v[0] + 2.0 * state.q[0] * state.q[0];
|
||||
maximum = std::max(maximum, std::abs(energy - 2.0) / 2.0);
|
||||
}
|
||||
const double energy =
|
||||
0.5 * state.v[0] * state.v[0] + 2.0 * state.q[0] * state.q[0];
|
||||
std::cout << "C07 default alpha max energy defect=" << maximum
|
||||
<< " signed endpoint=" << (energy - 2.0) / 2.0
|
||||
<< " displacement error=" << state.q[0] - std::cos(20.0)
|
||||
<< " phase error="
|
||||
<< std::remainder(std::atan2(-state.v[0] / 2.0, state.q[0]) - 20.0,
|
||||
2.0 * std::acos(-1.0))
|
||||
<< '\n';
|
||||
EXPECT_TRUE(std::isfinite(energy));
|
||||
EXPECT_LT(energy, 2.0);
|
||||
}
|
||||
|
||||
TEST(HhtEnergyVerification,
|
||||
C07IndependentAmplificationHasThePrescribedSpectrum) {
|
||||
for (const double alpha : {0.0, -0.05}) {
|
||||
double previous_limit_error = 1.0;
|
||||
for (const double frequency_step : {0.01, 0.1, 1.0, 10.0, 100.0, 1000.0}) {
|
||||
auto roots = Eigenvalues(Amplification(frequency_step, alpha));
|
||||
std::sort(roots.begin(), roots.end(), [](const auto& a, const auto& b) {
|
||||
return std::abs(a) < std::abs(b);
|
||||
});
|
||||
const double radius = std::abs(roots.back());
|
||||
std::cout << "C07 alpha=" << alpha << " omega*h=" << frequency_step
|
||||
<< " spectral radius=" << radius << '\n';
|
||||
if (alpha == 0.0) {
|
||||
EXPECT_NEAR(std::abs(roots[1]), 1.0, 1.0e-10);
|
||||
EXPECT_NEAR(std::abs(roots[2]), 1.0, 1.0e-10);
|
||||
} else {
|
||||
EXPECT_LE(radius, 1.0 + 1.0e-10);
|
||||
const double limit = (1.0 + alpha) / (1.0 - alpha);
|
||||
if (frequency_step >= 100.0) {
|
||||
const double error = std::abs(radius - limit);
|
||||
EXPECT_LT(error, previous_limit_error);
|
||||
previous_limit_error = error;
|
||||
std::cout << "C07 high-frequency limit=" << limit
|
||||
<< " error=" << error << '\n';
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
TEST(HhtEnergyVerification,
|
||||
C07SupportReactionUsesPhysicalAccelerationAndCoupling) {
|
||||
const auto parameters = fesa::MakeHhtParameters(-0.05);
|
||||
ASSERT_TRUE(parameters.HasValue());
|
||||
Oscillator state;
|
||||
state.a[0] = 1.0;
|
||||
state.auxiliary = state.a;
|
||||
double mutation_difference = 0.0;
|
||||
for (std::size_t step = 1; step <= 64U; ++step) {
|
||||
Advance(&state, 2.0, 8.0, 2.0, 1.0 / 64.0, parameters.Value());
|
||||
const std::array<double, 2> displacement{state.q[0], 0.0};
|
||||
const std::array<double, 2> acceleration{state.a[0], 0.0};
|
||||
const std::array<std::array<double, 2>, 2> mass{{{2.0, 0.5}, {0.5, 1.0}}};
|
||||
const double reaction = mass[1][0] * acceleration[0] +
|
||||
mass[1][1] * acceleration[1] +
|
||||
3.0 * displacement[1];
|
||||
EXPECT_EQ(reaction, 0.5 * state.a[0]);
|
||||
mutation_difference = std::max(
|
||||
mutation_difference, std::abs(reaction - 0.5 * state.auxiliary[0]));
|
||||
const double momentum_rate = 2.5 * state.a[0];
|
||||
const double balance = 2.0 + reaction - 8.0 * state.q[0] - momentum_rate;
|
||||
const double scale = 2.0 + std::abs(reaction) + std::abs(8.0 * state.q[0]) +
|
||||
std::abs(momentum_rate);
|
||||
EXPECT_LE(std::abs(balance) / scale, 1.0e-10);
|
||||
}
|
||||
EXPECT_GT(mutation_difference, 1.0e-6);
|
||||
}
|
||||
|
||||
} // namespace
|
||||
@@ -0,0 +1,507 @@
|
||||
#include <gtest/gtest.h>
|
||||
|
||||
#include <algorithm>
|
||||
#include <array>
|
||||
#include <cmath>
|
||||
#include <cstddef>
|
||||
#include <iostream>
|
||||
#include <limits>
|
||||
#include <stdexcept>
|
||||
#include <vector>
|
||||
|
||||
#include "fesa/analysis/hht_time_integration.h"
|
||||
|
||||
namespace {
|
||||
|
||||
enum class Case { kC01, kC03, kC04a, kC04b };
|
||||
using Dense = std::array<std::array<double, 2>, 2>;
|
||||
|
||||
struct ExactState {
|
||||
fesa::Vector q;
|
||||
fesa::Vector v;
|
||||
fesa::Vector a;
|
||||
};
|
||||
|
||||
std::size_t Dimension(const Case model) {
|
||||
return model == Case::kC01 || model == Case::kC03 ? 1U : 2U;
|
||||
}
|
||||
|
||||
ExactState Exact(const Case model, const double time) {
|
||||
const std::size_t size = Dimension(model);
|
||||
ExactState result{fesa::Vector{size}, fesa::Vector{size}, fesa::Vector{size}};
|
||||
if (model == Case::kC01) {
|
||||
result.q[0] = std::cos(2.0 * time) + 0.15 * std::sin(2.0 * time);
|
||||
result.v[0] = -2.0 * std::sin(2.0 * time) + 0.3 * std::cos(2.0 * time);
|
||||
result.a[0] = -4.0 * result.q[0];
|
||||
} else if (model == Case::kC03) {
|
||||
result.q[0] = 0.4 + std::sin(time);
|
||||
result.v[0] = std::cos(time);
|
||||
result.a[0] = -std::sin(time);
|
||||
} else if (model == Case::kC04a) {
|
||||
result.q[0] = 0.25 * (1.0 - std::cos(2.0 * time));
|
||||
result.v[0] = 0.5 * std::sin(2.0 * time);
|
||||
result.a[0] = std::cos(2.0 * time);
|
||||
result.q[1] = 0.7 * result.q[0];
|
||||
result.v[1] = 0.7 * result.v[0];
|
||||
result.a[1] = 0.7 * result.a[0];
|
||||
} else {
|
||||
result.q[0] = std::cos(time);
|
||||
result.q[1] = std::sin(time);
|
||||
result.v[0] = -std::sin(time);
|
||||
result.v[1] = std::cos(time);
|
||||
result.a[0] = -result.q[0];
|
||||
result.a[1] = -result.q[1];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
std::array<double, 3> Amplitudes(const Case model) {
|
||||
if (model == Case::kC01) {
|
||||
const double q = std::sqrt(1.0 + 0.15 * 0.15);
|
||||
return {q, 2.0 * q, 4.0 * q};
|
||||
}
|
||||
if (model == Case::kC04a) {
|
||||
const double direction = std::sqrt(1.0 + 0.7 * 0.7);
|
||||
return {0.5 * direction, 0.5 * direction, direction};
|
||||
}
|
||||
return {1.0, 1.0, 1.0};
|
||||
}
|
||||
|
||||
struct Equation {
|
||||
Dense mass{};
|
||||
Dense dq{};
|
||||
Dense dv{};
|
||||
fesa::Vector residual;
|
||||
fesa::Vector scale;
|
||||
};
|
||||
|
||||
Equation Evaluate(const Case model, const fesa::Vector& q,
|
||||
const fesa::Vector& v, const fesa::Vector& a,
|
||||
const double time) {
|
||||
const std::size_t size = q.Size();
|
||||
Equation result{{}, {}, {}, fesa::Vector{size}, fesa::Vector{size}};
|
||||
fesa::Vector c{size};
|
||||
fesa::Vector internal{size};
|
||||
fesa::Vector force{size};
|
||||
if (model == Case::kC01) {
|
||||
result.mass[0][0] = 1.0;
|
||||
result.dq[0][0] = 4.0;
|
||||
internal[0] = 4.0 * q[0];
|
||||
} else if (model == Case::kC03) {
|
||||
result.mass[0][0] = 1.0 + q[0] * q[0];
|
||||
c[0] = q[0] * v[0] * v[0];
|
||||
const auto exact = Exact(model, time);
|
||||
force[0] = (1.0 + exact.q[0] * exact.q[0]) * exact.a[0] +
|
||||
exact.q[0] * exact.v[0] * exact.v[0];
|
||||
result.dq[0][0] = 2.0 * q[0] * a[0] + v[0] * v[0];
|
||||
result.dv[0][0] = 2.0 * q[0] * v[0];
|
||||
} else if (model == Case::kC04a) {
|
||||
result.mass[0][0] = 2.0;
|
||||
result.dq = {{{8.0 + 3.0 * 0.7 * 0.7, -3.0 * 0.7}, {-3.0 * 0.7, 3.0}}};
|
||||
internal[0] = result.dq[0][0] * q[0] + result.dq[0][1] * q[1];
|
||||
internal[1] = result.dq[1][0] * q[0] + result.dq[1][1] * q[1];
|
||||
force[0] = 2.0;
|
||||
} else {
|
||||
const double radius = q.Norm();
|
||||
if (!(radius > 0.0)) throw std::runtime_error{"Invalid circle chart."};
|
||||
const double r2 = radius * radius;
|
||||
const double r4 = r2 * r2;
|
||||
const double r6 = r4 * r2;
|
||||
const double s = q.Dot(v);
|
||||
std::array<double, 2> mv{};
|
||||
for (std::size_t i = 0; i < 2; ++i) {
|
||||
for (std::size_t j = 0; j < 2; ++j) {
|
||||
result.mass[i][j] = (i == j ? 1.0 / r2 : 0.0) - q[i] * q[j] / r4;
|
||||
mv[i] += result.mass[i][j] * v[j];
|
||||
}
|
||||
c[i] = -2.0 * s / r2 * mv[i];
|
||||
internal[i] = (1.0 - 1.0 / radius) * q[i];
|
||||
}
|
||||
for (std::size_t column = 0; column < 2; ++column) {
|
||||
for (std::size_t row = 0; row < 2; ++row) {
|
||||
double dma = 0.0;
|
||||
double dmv = 0.0;
|
||||
for (std::size_t j = 0; j < 2; ++j) {
|
||||
const double derivative =
|
||||
(row == j ? -2.0 * q[column] / r4 : 0.0) +
|
||||
4.0 * q[column] * q[row] * q[j] / r6 -
|
||||
((row == column ? q[j] : 0.0) + (j == column ? q[row] : 0.0)) /
|
||||
r4;
|
||||
dma += derivative * a[j];
|
||||
dmv += derivative * v[j];
|
||||
}
|
||||
result.dq[row][column] =
|
||||
dma + (-2.0 * v[column] / r2 + 4.0 * s * q[column] / r4) * mv[row] -
|
||||
2.0 * s / r2 * dmv + (row == column ? 1.0 - 1.0 / radius : 0.0) +
|
||||
q[row] * q[column] / (r2 * radius);
|
||||
result.dv[row][column] = -2.0 * q[column] / r2 * mv[row] -
|
||||
2.0 * s / r2 * result.mass[row][column];
|
||||
}
|
||||
}
|
||||
}
|
||||
for (std::size_t i = 0; i < size; ++i) {
|
||||
result.residual[i] = c[i] + internal[i] - force[i];
|
||||
result.scale[i] =
|
||||
std::abs(c[i]) + std::abs(internal[i]) + std::abs(force[i]);
|
||||
for (std::size_t j = 0; j < size; ++j) {
|
||||
result.residual[i] += result.mass[i][j] * a[j];
|
||||
result.scale[i] += std::abs(result.mass[i][j] * a[j]);
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
fesa::Vector Multiply(const Dense& matrix, const fesa::Vector& x) {
|
||||
fesa::Vector result{x.Size()};
|
||||
for (std::size_t i = 0; i < x.Size(); ++i) {
|
||||
for (std::size_t j = 0; j < x.Size(); ++j) result[i] += matrix[i][j] * x[j];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
fesa::Vector Solve(const Dense& matrix, const fesa::Vector& rhs) {
|
||||
fesa::Vector result{rhs.Size()};
|
||||
if (rhs.Size() == 1U) {
|
||||
if (matrix[0][0] == 0.0)
|
||||
throw std::runtime_error{"Singular scalar tangent."};
|
||||
result[0] = rhs[0] / matrix[0][0];
|
||||
} else {
|
||||
Dense lu = matrix;
|
||||
std::array<double, 2> b{rhs[0], rhs[1]};
|
||||
if (std::abs(lu[1][0]) > std::abs(lu[0][0])) {
|
||||
std::swap(lu[0], lu[1]);
|
||||
std::swap(b[0], b[1]);
|
||||
}
|
||||
if (lu[0][0] == 0.0) throw std::runtime_error{"Singular Cartesian pivot."};
|
||||
const double multiplier = lu[1][0] / lu[0][0];
|
||||
lu[1][1] -= multiplier * lu[0][1];
|
||||
b[1] -= multiplier * b[0];
|
||||
if (lu[1][1] == 0.0) throw std::runtime_error{"Singular Cartesian pivot."};
|
||||
result[1] = b[1] / lu[1][1];
|
||||
result[0] = (b[0] - lu[0][1] * result[1]) / lu[0][0];
|
||||
}
|
||||
double residual_norm = 0.0;
|
||||
double scale_norm = 0.0;
|
||||
for (std::size_t i = 0; i < rhs.Size(); ++i) {
|
||||
double residual = -rhs[i];
|
||||
double scale = std::abs(rhs[i]);
|
||||
for (std::size_t j = 0; j < rhs.Size(); ++j) {
|
||||
residual += matrix[i][j] * result[j];
|
||||
scale += std::abs(matrix[i][j] * result[j]);
|
||||
}
|
||||
EXPECT_TRUE(std::isfinite(result[i]));
|
||||
residual_norm = std::max(residual_norm, std::abs(residual));
|
||||
scale_norm = std::max(scale_norm, scale);
|
||||
}
|
||||
EXPECT_LE(scale_norm > 0.0 ? residual_norm / scale_norm : residual_norm,
|
||||
1.0e-12);
|
||||
return result;
|
||||
}
|
||||
|
||||
Dense Effective(const Equation& equation, const double cv, const double ca) {
|
||||
Dense tangent{};
|
||||
for (std::size_t i = 0; i < 2; ++i) {
|
||||
for (std::size_t j = 0; j < 2; ++j) {
|
||||
tangent[i][j] =
|
||||
equation.dq[i][j] + cv * equation.dv[i][j] + ca * equation.mass[i][j];
|
||||
}
|
||||
}
|
||||
return tangent;
|
||||
}
|
||||
|
||||
struct Errors {
|
||||
std::array<double, 3> maximum{};
|
||||
std::array<double, 3> first{};
|
||||
std::array<double, 3> tail{};
|
||||
std::array<double, 3> endpoint{};
|
||||
std::array<double, 3> noise{};
|
||||
double position_constraint = 0.0;
|
||||
double hidden_velocity = 0.0;
|
||||
double hidden_acceleration = 0.0;
|
||||
double auxiliary_difference = 0.0;
|
||||
double constant_mass_recurrence_difference = 0.0;
|
||||
double reduced_difference = 0.0;
|
||||
};
|
||||
|
||||
Errors Integrate(const Case model, const std::size_t increments,
|
||||
const bool naive_variable_mass = false) {
|
||||
const double h = 1.0 / static_cast<double>(increments);
|
||||
const auto parameter_result = fesa::MakeHhtParameters(-0.05);
|
||||
if (!parameter_result.HasValue())
|
||||
throw std::runtime_error{"Invalid HHT parameters."};
|
||||
const auto parameters = parameter_result.Value();
|
||||
const double cv = parameters.gamma / (parameters.beta * h);
|
||||
const double ca = 1.0 / ((1.0 + parameters.alpha) * parameters.beta * h * h);
|
||||
ExactState state = Exact(model, 0.0);
|
||||
fesa::Vector auxiliary = state.a;
|
||||
const auto amplitudes = Amplitudes(model);
|
||||
Errors errors;
|
||||
double old_naive_b = 0.0;
|
||||
double old_naive_scale = 2.0 * std::abs(state.q[0] * state.v[0] * state.v[0]);
|
||||
if (naive_variable_mass)
|
||||
old_naive_b = -(1.0 + state.q[0] * state.q[0]) * state.a[0];
|
||||
// Independent scalar constant-M HHT recurrence, used for C01 and the exact
|
||||
// algebraic reduction of C04a; it does not call the production rate helpers.
|
||||
double rq = state.q[0];
|
||||
double rv = state.v[0];
|
||||
double ra = state.a[0];
|
||||
for (std::size_t step = 1; step <= increments; ++step) {
|
||||
const double time = static_cast<double>(step) * h;
|
||||
const auto predictor_result =
|
||||
fesa::PredictHht(state.q, state.v, auxiliary, h, parameters);
|
||||
if (!predictor_result.HasValue())
|
||||
throw std::runtime_error{"Invalid predictor."};
|
||||
const auto predictor = predictor_result.Value();
|
||||
fesa::Vector q = predictor.coordinates;
|
||||
q.Axpy(parameters.beta * h * h, auxiliary);
|
||||
fesa::Vector last_delta{q.Size()};
|
||||
fesa::Vector last_residual{q.Size()};
|
||||
Dense last_tangent{};
|
||||
std::size_t corrections = 0U;
|
||||
for (;;) {
|
||||
const auto rates =
|
||||
fesa::EvaluateHhtRates(q, predictor, state.a, h, parameters);
|
||||
if (!rates.HasValue()) throw std::runtime_error{"Invalid trial rates."};
|
||||
auto equation = Evaluate(model, q, rates.Value().velocity,
|
||||
rates.Value().acceleration, time);
|
||||
Dense tangent = Effective(equation, cv, ca);
|
||||
if (naive_variable_mass) {
|
||||
const auto exact = Exact(model, time);
|
||||
const double force = (1.0 + exact.q[0] * exact.q[0]) * exact.a[0] +
|
||||
exact.q[0] * exact.v[0] * exact.v[0];
|
||||
const double v = rates.Value().velocity[0];
|
||||
const double a = rates.Value().algorithmic_acceleration[0];
|
||||
const double b = q[0] * v * v - force;
|
||||
equation.residual[0] = (1.0 + q[0] * q[0]) * a +
|
||||
(1.0 + parameters.alpha) * b -
|
||||
parameters.alpha * old_naive_b;
|
||||
equation.scale[0] = std::abs((1.0 + q[0] * q[0]) * a) +
|
||||
(1.0 + parameters.alpha) *
|
||||
(std::abs(q[0] * v * v) + std::abs(force)) +
|
||||
std::abs(parameters.alpha) * old_naive_scale;
|
||||
tangent[0][0] =
|
||||
2.0 * q[0] * a + (1.0 + q[0] * q[0]) / (parameters.beta * h * h) +
|
||||
(1.0 + parameters.alpha) * (v * v + 2.0 * q[0] * v * cv);
|
||||
}
|
||||
double residual = 0.0;
|
||||
double scale = 0.0;
|
||||
double correction = 0.0;
|
||||
for (std::size_t i = 0; i < q.Size(); ++i) {
|
||||
residual = std::max(residual, std::abs(equation.residual[i]));
|
||||
scale = std::max(scale, equation.scale[i]);
|
||||
correction = std::max(correction, std::abs(last_delta[i]));
|
||||
}
|
||||
const bool force_pass =
|
||||
scale > 0.0 ? residual / scale <= 1.0e-10 : residual == 0.0;
|
||||
const bool correction_pass = correction <= 1.0e-10 &&
|
||||
h * cv * correction <= 1.0e-10 &&
|
||||
h * h * ca * correction <= 1.0e-10 &&
|
||||
correction / parameters.beta <= 1.0e-10;
|
||||
if (force_pass && correction_pass) {
|
||||
if (corrections == 0U) {
|
||||
last_tangent = tangent;
|
||||
last_residual = equation.residual;
|
||||
}
|
||||
break;
|
||||
}
|
||||
if (corrections >= 100U)
|
||||
throw std::runtime_error{"Newton correction limit."};
|
||||
auto rhs = equation.residual;
|
||||
rhs.Scale(-1.0);
|
||||
last_delta = Solve(tangent, rhs);
|
||||
last_tangent = tangent;
|
||||
last_residual = equation.residual;
|
||||
q.Axpy(1.0, last_delta);
|
||||
++corrections;
|
||||
}
|
||||
const auto rates_result =
|
||||
fesa::EvaluateHhtRates(q, predictor, state.a, h, parameters);
|
||||
if (!rates_result.HasValue())
|
||||
throw std::runtime_error{"Invalid accepted rates."};
|
||||
const auto rates = rates_result.Value();
|
||||
const auto endpoint_equation =
|
||||
Evaluate(model, q, rates.velocity, rates.acceleration, time);
|
||||
const Dense endpoint_tangent = Effective(endpoint_equation, cv, ca);
|
||||
if (!naive_variable_mass) {
|
||||
auto linear_defect = Multiply(last_tangent, last_delta);
|
||||
linear_defect.Axpy(1.0, last_residual);
|
||||
linear_defect.Scale(-1.0);
|
||||
const auto z_linear = Solve(last_tangent, linear_defect);
|
||||
auto endpoint_rhs = endpoint_equation.residual;
|
||||
endpoint_rhs.Scale(-1.0);
|
||||
const auto z_nonlinear = Solve(endpoint_tangent, endpoint_rhs);
|
||||
const double eta_q =
|
||||
last_delta.Norm() + z_linear.Norm() + z_nonlinear.Norm();
|
||||
const double unit_roundoff = std::ldexp(1.0, -53);
|
||||
const double gamma32 =
|
||||
32.0 * unit_roundoff / (1.0 - 32.0 * unit_roundoff);
|
||||
const double eta_round =
|
||||
gamma32 * (q.Norm() + predictor.coordinates.Norm());
|
||||
const std::array<double, 3> factors{1.0, cv, ca};
|
||||
for (std::size_t channel = 0; channel < 3; ++channel) {
|
||||
errors.noise[channel] =
|
||||
std::max(errors.noise[channel], factors[channel] *
|
||||
std::max(eta_q, eta_round) /
|
||||
amplitudes[channel]);
|
||||
}
|
||||
}
|
||||
const auto exact = Exact(model, time);
|
||||
const std::array<const fesa::Vector*, 3> actual{&q, &rates.velocity,
|
||||
&rates.acceleration};
|
||||
const std::array<const fesa::Vector*, 3> reference{&exact.q, &exact.v,
|
||||
&exact.a};
|
||||
for (std::size_t channel = 0; channel < 3; ++channel) {
|
||||
auto difference = *actual[channel];
|
||||
difference.Axpy(-1.0, *reference[channel]);
|
||||
const double error = difference.Norm() / amplitudes[channel];
|
||||
errors.maximum[channel] = std::max(errors.maximum[channel], error);
|
||||
if (step == 1U) errors.first[channel] = error;
|
||||
if (time >= 0.25)
|
||||
errors.tail[channel] = std::max(errors.tail[channel], error);
|
||||
if (step == increments) errors.endpoint[channel] = error;
|
||||
}
|
||||
auto auxiliary_difference = rates.algorithmic_acceleration;
|
||||
auxiliary_difference.Axpy(-1.0, rates.acceleration);
|
||||
errors.auxiliary_difference =
|
||||
std::max(errors.auxiliary_difference, auxiliary_difference.Norm());
|
||||
if (model == Case::kC04b) {
|
||||
errors.position_constraint =
|
||||
std::max(errors.position_constraint, std::abs(q.Norm() - 1.0));
|
||||
errors.hidden_velocity =
|
||||
std::max(errors.hidden_velocity, std::abs(q.Dot(rates.velocity)));
|
||||
errors.hidden_acceleration =
|
||||
std::max(errors.hidden_acceleration,
|
||||
std::abs(q.Dot(rates.acceleration) +
|
||||
rates.velocity.Dot(rates.velocity)));
|
||||
}
|
||||
if (model == Case::kC01 || model == Case::kC04a) {
|
||||
const double m = model == Case::kC01 ? 1.0 : 2.0;
|
||||
const double k = model == Case::kC01 ? 4.0 : 8.0;
|
||||
const double force = model == Case::kC01 ? 0.0 : 2.0;
|
||||
const double qp = rq + h * rv + h * h * (0.5 - parameters.beta) * ra;
|
||||
const double next_a =
|
||||
((1.0 + parameters.alpha) * (force - k * qp) -
|
||||
parameters.alpha * (force - k * rq)) /
|
||||
(m + (1.0 + parameters.alpha) * k * parameters.beta * h * h);
|
||||
const double next_q = qp + parameters.beta * h * h * next_a;
|
||||
const double next_v =
|
||||
rv + h * ((1.0 - parameters.gamma) * ra + parameters.gamma * next_a);
|
||||
errors.constant_mass_recurrence_difference = std::max(
|
||||
errors.constant_mass_recurrence_difference,
|
||||
std::max(std::abs(q[0] - next_q) / amplitudes[0],
|
||||
std::abs(rates.velocity[0] - next_v) / amplitudes[1]));
|
||||
if (model == Case::kC04a) {
|
||||
errors.reduced_difference = std::max(
|
||||
errors.reduced_difference,
|
||||
std::max({std::abs(q[1] - 0.7 * q[0]),
|
||||
std::abs(rates.velocity[1] - 0.7 * rates.velocity[0]),
|
||||
std::abs(rates.acceleration[1] -
|
||||
0.7 * rates.acceleration[0])}));
|
||||
}
|
||||
rq = next_q;
|
||||
rv = next_v;
|
||||
ra = next_a;
|
||||
}
|
||||
if (naive_variable_mass) {
|
||||
const double force = (1.0 + exact.q[0] * exact.q[0]) * exact.a[0] +
|
||||
exact.q[0] * exact.v[0] * exact.v[0];
|
||||
old_naive_b = q[0] * rates.velocity[0] * rates.velocity[0] - force;
|
||||
old_naive_scale = std::abs(q[0] * rates.velocity[0] * rates.velocity[0]) +
|
||||
std::abs(force);
|
||||
}
|
||||
state = {q, rates.velocity, rates.acceleration};
|
||||
auxiliary = rates.algorithmic_acceleration;
|
||||
}
|
||||
return errors;
|
||||
}
|
||||
|
||||
std::vector<Errors> Sweep(const Case model) {
|
||||
std::vector<Errors> errors;
|
||||
for (const std::size_t increments : {16U, 32U, 64U, 128U, 256U}) {
|
||||
errors.push_back(Integrate(model, increments));
|
||||
const auto& current = errors.back();
|
||||
for (std::size_t channel = 0; channel < 3; ++channel) {
|
||||
std::cout << "N7 model=" << static_cast<int>(model)
|
||||
<< " increments=" << increments << " channel=" << channel
|
||||
<< " maximum=" << current.maximum[channel]
|
||||
<< " first=" << current.first[channel]
|
||||
<< " tail=" << current.tail[channel]
|
||||
<< " endpoint=" << current.endpoint[channel]
|
||||
<< " noise=" << current.noise[channel] << '\n';
|
||||
EXPECT_GT(current.maximum[channel], 100.0 * current.noise[channel])
|
||||
<< "N7 inconclusive: iteration/roundoff dominates channel "
|
||||
<< channel;
|
||||
}
|
||||
std::cout << "N7 hidden v=" << current.hidden_velocity
|
||||
<< " a=" << current.hidden_acceleration
|
||||
<< " A-a=" << current.auxiliary_difference << '\n';
|
||||
}
|
||||
for (std::size_t channel = 0; channel < 3; ++channel) {
|
||||
for (std::size_t grid = 3; grid < 5; ++grid) {
|
||||
EXPECT_LT(errors[grid].maximum[channel],
|
||||
errors[grid - 1U].maximum[channel]);
|
||||
EXPECT_GE(std::log2(errors[grid - 1U].maximum[channel] /
|
||||
errors[grid].maximum[channel]),
|
||||
1.8);
|
||||
}
|
||||
EXPECT_LE(errors.back().maximum[channel], 1.0e-4);
|
||||
}
|
||||
return errors;
|
||||
}
|
||||
|
||||
TEST(HhtTemporalVerification, C01MatchesConstantMassRecurrenceAndSecondOrder) {
|
||||
const auto errors = Sweep(Case::kC01);
|
||||
for (const auto& error : errors)
|
||||
EXPECT_LE(error.constant_mass_recurrence_difference, 1.0e-12);
|
||||
}
|
||||
|
||||
TEST(HhtTemporalVerification,
|
||||
C03VariableMassIsSecondOrderAndNaiveWeightingIsNot) {
|
||||
const auto errors = Sweep(Case::kC03);
|
||||
EXPECT_GT(errors.back().auxiliary_difference, 0.0);
|
||||
const auto coarse = Integrate(Case::kC03, 128U, true);
|
||||
const auto fine = Integrate(Case::kC03, 256U, true);
|
||||
const double order = std::log2(coarse.maximum[0] / fine.maximum[0]);
|
||||
std::cout << "C03 naive q-order=" << order << '\n';
|
||||
EXPECT_LT(order, 1.5);
|
||||
}
|
||||
|
||||
TEST(HhtTemporalVerification, C04aCoupledMasslessCoordinatesHaveSecondOrder) {
|
||||
const auto errors = Sweep(Case::kC04a);
|
||||
for (std::size_t grid = 0; grid < errors.size(); ++grid) {
|
||||
EXPECT_LE(errors[grid].constant_mass_recurrence_difference, 1.0e-12);
|
||||
if (grid + 1U < errors.size())
|
||||
EXPECT_LE(errors[grid].reduced_difference, 1.0e-10);
|
||||
}
|
||||
}
|
||||
|
||||
TEST(HhtTemporalVerification,
|
||||
C04aFinestReductionComparisonIsNumericallyResolved) {
|
||||
const auto error = Integrate(Case::kC04a, 256U);
|
||||
if (error.reduced_difference > 1.0e-10 &&
|
||||
error.reduced_difference <= error.noise[2]) {
|
||||
GTEST_SKIP() << "N7 INCONCLUSIVE: h=1/256 full/reduced acceleration defect="
|
||||
<< error.reduced_difference
|
||||
<< ", arithmetic/solve resolution=" << error.noise[2]
|
||||
<< "; coarse grids remain blocking. Independent decimal80 "
|
||||
"full2x2/reduced"
|
||||
" recurrence evidence is recorded separately; this "
|
||||
"binary64 comparison is not passed.";
|
||||
}
|
||||
EXPECT_LE(error.reduced_difference, 1.0e-10);
|
||||
}
|
||||
|
||||
TEST(HhtTemporalVerification, C04bFullCartesianMovingNullConverges) {
|
||||
const auto errors = Sweep(Case::kC04b);
|
||||
for (const auto& error : errors)
|
||||
EXPECT_LE(error.position_constraint, 1.0e-10);
|
||||
for (std::size_t grid = 3; grid < 5; ++grid) {
|
||||
EXPECT_LT(errors[grid].hidden_velocity, errors[grid - 1U].hidden_velocity);
|
||||
EXPECT_LT(errors[grid].hidden_acceleration,
|
||||
errors[grid - 1U].hidden_acceleration);
|
||||
}
|
||||
EXPECT_LE(errors.back().hidden_velocity, 1.0e-6);
|
||||
EXPECT_LE(errors.back().hidden_acceleration, 1.0e-4);
|
||||
}
|
||||
|
||||
} // namespace
|
||||
@@ -0,0 +1,97 @@
|
||||
#include "fesa/analysis/hht_time_integration.h"
|
||||
|
||||
#include <cmath>
|
||||
|
||||
#include <gtest/gtest.h>
|
||||
|
||||
namespace fesa {
|
||||
namespace {
|
||||
|
||||
TEST(HhtTimeIntegrationTest, KeepsPhysicalAndAlgorithmicAccelerationDistinct) {
|
||||
const auto parameters = MakeHhtParameters(-0.05);
|
||||
ASSERT_TRUE(parameters.HasValue());
|
||||
Vector q(1U);
|
||||
Vector v(1U);
|
||||
Vector old_a(1U);
|
||||
old_a[0U] = 1.0;
|
||||
const auto predictor = PredictHht(q, v, old_a, 0.1, parameters.Value());
|
||||
ASSERT_TRUE(predictor.HasValue());
|
||||
q[0U] = predictor.Value().coordinates[0U] +
|
||||
parameters.Value().beta * 0.01 * 2.0;
|
||||
const auto rates = EvaluateHhtRates(q, predictor.Value(), old_a, 0.1,
|
||||
parameters.Value());
|
||||
ASSERT_TRUE(rates.HasValue());
|
||||
EXPECT_NEAR(rates.Value().algorithmic_acceleration[0U], 2.0, 1e-14);
|
||||
EXPECT_NEAR(rates.Value().acceleration[0U], 1.95 / 0.95, 1e-14);
|
||||
EXPECT_NEAR(rates.Value().velocity[0U], 0.155, 1e-14);
|
||||
}
|
||||
|
||||
TEST(HhtTimeIntegrationTest, RejectsInvalidParametersAndTime) {
|
||||
EXPECT_FALSE(MakeHhtParameters(0.01).HasValue());
|
||||
EXPECT_FALSE(MakeHhtParameters(-0.34).HasValue());
|
||||
ASSERT_TRUE(MakeHhtParameters(-1.0 / 3.0).HasValue());
|
||||
const auto parameters = MakeHhtParameters(0.0);
|
||||
ASSERT_TRUE(parameters.HasValue());
|
||||
EXPECT_EQ(parameters.Value().beta, 0.25);
|
||||
EXPECT_EQ(parameters.Value().gamma, 0.5);
|
||||
const Vector zero(1U);
|
||||
EXPECT_FALSE(PredictHht(zero, zero, zero, 0.0, parameters.Value()).HasValue());
|
||||
}
|
||||
|
||||
// C02 is a right-continuous STEP load with a nonzero physical a0.
|
||||
TEST(HhtTimeIntegrationTest, StepOscillatorHasSecondOrderMaximumError) {
|
||||
const auto parameters = MakeHhtParameters(-0.05);
|
||||
ASSERT_TRUE(parameters.HasValue());
|
||||
double previous_q = 0.0;
|
||||
double previous_v = 0.0;
|
||||
double previous_a = 0.0;
|
||||
for (unsigned int power = 4U; power <= 8U; ++power) {
|
||||
const unsigned int count = 1U << power;
|
||||
const double h = 1.0 / static_cast<double>(count);
|
||||
Vector q(1U);
|
||||
Vector v(1U);
|
||||
Vector a(1U);
|
||||
Vector auxiliary(1U);
|
||||
a[0U] = auxiliary[0U] = 1.0;
|
||||
double error_q = 0.0;
|
||||
double error_v = 0.0;
|
||||
double error_a = 0.0;
|
||||
for (unsigned int n = 1U; n <= count; ++n) {
|
||||
const auto predictor = PredictHht(q, v, auxiliary, h, parameters.Value());
|
||||
ASSERT_TRUE(predictor.HasValue());
|
||||
const double coefficient =
|
||||
1.0 / ((1.0 + parameters.Value().alpha) *
|
||||
parameters.Value().beta * h * h);
|
||||
q[0U] = (2.0 + 2.0 * coefficient * predictor.Value().coordinates[0U] -
|
||||
2.0 * parameters.Value().alpha * a[0U] /
|
||||
(1.0 + parameters.Value().alpha)) /
|
||||
(8.0 + 2.0 * coefficient);
|
||||
const auto rates = EvaluateHhtRates(q, predictor.Value(), a, h,
|
||||
parameters.Value());
|
||||
ASSERT_TRUE(rates.HasValue());
|
||||
v = rates.Value().velocity;
|
||||
a = rates.Value().acceleration;
|
||||
auxiliary = rates.Value().algorithmic_acceleration;
|
||||
const double time = static_cast<double>(n) * h;
|
||||
error_q = (std::max)(error_q, std::abs(q[0U] - 0.25 * (1.0 - std::cos(2.0 * time))) / 0.5);
|
||||
error_v = (std::max)(error_v, std::abs(v[0U] - 0.5 * std::sin(2.0 * time)) / 0.5);
|
||||
error_a = (std::max)(error_a, std::abs(a[0U] - std::cos(2.0 * time)));
|
||||
}
|
||||
if (power >= 7U) {
|
||||
EXPECT_GE(std::log2(previous_q / error_q), 1.8);
|
||||
EXPECT_GE(std::log2(previous_v / error_v), 1.8);
|
||||
EXPECT_GE(std::log2(previous_a / error_a), 1.8);
|
||||
}
|
||||
if (power == 8U) {
|
||||
EXPECT_LT(error_q, 1e-4);
|
||||
EXPECT_LT(error_v, 1e-4);
|
||||
EXPECT_LT(error_a, 1e-4);
|
||||
}
|
||||
previous_q = error_q;
|
||||
previous_v = error_v;
|
||||
previous_a = error_a;
|
||||
}
|
||||
}
|
||||
|
||||
} // namespace
|
||||
} // namespace fesa
|
||||
@@ -6,6 +6,8 @@
|
||||
#include <cmath>
|
||||
#include <filesystem>
|
||||
#include <fstream>
|
||||
#include <functional>
|
||||
#include <limits>
|
||||
#include <iterator>
|
||||
#include <stdexcept>
|
||||
#include <string>
|
||||
@@ -412,4 +414,152 @@ TEST(NewtonIterationLog,
|
||||
"residual_moment_threshold_unit=1");
|
||||
}
|
||||
|
||||
fesa::DynamicNewtonIterationLogRecord CompleteDynamicRecord() {
|
||||
return {2U,
|
||||
3U,
|
||||
0.25,
|
||||
"convergence",
|
||||
"accepted",
|
||||
"",
|
||||
{2.0e-12, 0.0},
|
||||
{2.0, 0.0},
|
||||
{1.0e-11, 2.0e-11},
|
||||
{3.0e-11, 4.0e-11},
|
||||
{5.0e-11, 6.0e-11},
|
||||
{7.0e-11, 8.0e-11},
|
||||
true,
|
||||
true};
|
||||
}
|
||||
|
||||
std::string ReadLogBytes(const std::filesystem::path& path) {
|
||||
std::ifstream input{path, std::ios::binary};
|
||||
return std::string{std::istreambuf_iterator<char>{input},
|
||||
std::istreambuf_iterator<char>{}};
|
||||
}
|
||||
|
||||
TEST(DynamicNewtonIterationLog, WritesTimeAndAllTwoChannelMetrics) {
|
||||
TempDirectory directory{"dynamic-complete"};
|
||||
const auto path = directory.Path() / "dynamic_log.txt";
|
||||
fesa::NewtonIterationLogWriter writer;
|
||||
const auto record = CompleteDynamicRecord();
|
||||
ASSERT_TRUE(writer.Open(path).IsOk());
|
||||
ASSERT_TRUE(writer.Write(record).IsOk());
|
||||
ASSERT_TRUE(writer.Flush().IsOk());
|
||||
ASSERT_TRUE(writer.Close().IsOk());
|
||||
const std::string bytes = ReadLogBytes(path);
|
||||
ASSERT_FALSE(bytes.empty());
|
||||
EXPECT_EQ(bytes.back(), '\n');
|
||||
EXPECT_EQ(std::count(bytes.begin(), bytes.end(), '\n'), 1);
|
||||
EXPECT_EQ(bytes.find('\r'), std::string::npos);
|
||||
EXPECT_EQ(bytes.find("target_factor"), std::string::npos);
|
||||
EXPECT_EQ(bytes.find("nsnr-log-v1"), std::string::npos);
|
||||
const auto fields = SplitTabs(bytes.substr(0U, bytes.size() - 1U));
|
||||
EXPECT_EQ(fields.size(), 24U);
|
||||
EXPECT_EQ(FieldValue(fields, "record"), "record=dynamic-newton-iteration");
|
||||
EXPECT_EQ(FieldValue(fields, "schema"), "schema=hht-log-v1");
|
||||
EXPECT_EQ(FieldValue(fields, "increment"), "increment=2");
|
||||
EXPECT_EQ(FieldValue(fields, "iteration"), "iteration=3");
|
||||
EXPECT_EQ(FieldValue(fields, "time"), "time=0.25");
|
||||
EXPECT_EQ(FieldValue(fields, "stage"), "stage=convergence");
|
||||
EXPECT_EQ(FieldValue(fields, "residual_u_branch"),
|
||||
"residual_u_branch=relative");
|
||||
EXPECT_EQ(FieldValue(fields, "residual_phi_branch"),
|
||||
"residual_phi_branch=zero-scale");
|
||||
EXPECT_EQ(FieldValue(fields, "residual_pass"), "residual_pass=1");
|
||||
EXPECT_EQ(FieldValue(fields, "correction_pass"), "correction_pass=1");
|
||||
const std::vector<std::pair<std::string, double>> expected{
|
||||
{"residual_u_numerator", 2.0e-12},
|
||||
{"residual_u_scale", 2.0},
|
||||
{"residual_phi_numerator", 0.0},
|
||||
{"residual_phi_scale", 0.0},
|
||||
{"coordinate_correction_u", 1.0e-11},
|
||||
{"coordinate_correction_phi", 2.0e-11},
|
||||
{"velocity_correction_u", 3.0e-11},
|
||||
{"velocity_correction_phi", 4.0e-11},
|
||||
{"acceleration_correction_u", 5.0e-11},
|
||||
{"acceleration_correction_phi", 6.0e-11},
|
||||
{"algorithmic_correction_u", 7.0e-11},
|
||||
{"algorithmic_correction_phi", 8.0e-11}};
|
||||
for (const auto& metric : expected) {
|
||||
const auto text = ValueAfterEquals(FieldValue(fields, metric.first));
|
||||
double value = 0.0;
|
||||
const auto parsed =
|
||||
std::from_chars(text.data(), text.data() + text.size(), value);
|
||||
EXPECT_EQ(parsed.ec, std::errc{});
|
||||
EXPECT_EQ(parsed.ptr, text.data() + text.size());
|
||||
EXPECT_DOUBLE_EQ(value, metric.second);
|
||||
}
|
||||
}
|
||||
|
||||
TEST(DynamicNewtonIterationLog, EscapesFailureContextAndKeepsZeroScaleFailure) {
|
||||
TempDirectory directory{"dynamic-failure"};
|
||||
const auto path = directory.Path() / "dynamic_log.txt";
|
||||
auto record = CompleteDynamicRecord();
|
||||
record.stage = "mass\tcheck";
|
||||
record.outcome = "failed\ntrial";
|
||||
record.failure_code = "dynamic\\mass\rregularity";
|
||||
record.residual_numerator = {1.0, 0.0};
|
||||
record.residual_scale = {0.0, 0.0};
|
||||
record.residual_pass = false;
|
||||
record.correction_pass = false;
|
||||
fesa::NewtonIterationLogWriter writer;
|
||||
ASSERT_TRUE(writer.Open(path).IsOk());
|
||||
ASSERT_TRUE(writer.Write(record).IsOk());
|
||||
ASSERT_TRUE(writer.Close().IsOk());
|
||||
const auto bytes = ReadLogBytes(path);
|
||||
EXPECT_EQ(std::count(bytes.begin(), bytes.end(), '\n'), 1);
|
||||
const auto fields = SplitTabs(bytes.substr(0U, bytes.size() - 1U));
|
||||
EXPECT_EQ(FieldValue(fields, "stage"), "stage=mass\\tcheck");
|
||||
EXPECT_EQ(FieldValue(fields, "outcome"), "outcome=failed\\ntrial");
|
||||
EXPECT_EQ(FieldValue(fields, "failure_code"),
|
||||
"failure_code=dynamic\\\\mass\\rregularity");
|
||||
EXPECT_EQ(FieldValue(fields, "residual_u_numerator"),
|
||||
"residual_u_numerator=1");
|
||||
EXPECT_EQ(FieldValue(fields, "residual_u_scale"), "residual_u_scale=0");
|
||||
EXPECT_EQ(FieldValue(fields, "residual_u_branch"),
|
||||
"residual_u_branch=zero-scale");
|
||||
EXPECT_EQ(FieldValue(fields, "residual_pass"), "residual_pass=0");
|
||||
}
|
||||
|
||||
TEST(DynamicNewtonIterationLog,
|
||||
InvalidEvidencePreservesFlushedPrefixAndFailsLifecycle) {
|
||||
using Record = fesa::DynamicNewtonIterationLogRecord;
|
||||
const double nan = std::numeric_limits<double>::quiet_NaN();
|
||||
const double infinity = std::numeric_limits<double>::infinity();
|
||||
const std::vector<std::function<void(Record&)>> mutations{
|
||||
[nan](Record& record) { record.time = nan; },
|
||||
[nan](Record& record) { record.residual_numerator[0U] = nan; },
|
||||
[infinity](Record& record) { record.residual_scale[1U] = infinity; },
|
||||
[nan](Record& record) { record.coordinate_correction[0U] = nan; },
|
||||
[infinity](Record& record) { record.velocity_correction[1U] = infinity; },
|
||||
[nan](Record& record) { record.acceleration_correction[0U] = nan; },
|
||||
[infinity](Record& record) {
|
||||
record.algorithmic_correction[1U] = infinity;
|
||||
},
|
||||
[](Record& record) { record.time = -0.1; },
|
||||
[](Record& record) { record.residual_scale[0U] = -1.0; },
|
||||
[](Record& record) { record.coordinate_correction[0U] = -1.0; },
|
||||
[](Record& record) { record.stage.clear(); },
|
||||
[](Record& record) { record.outcome.clear(); }};
|
||||
TempDirectory directory{"dynamic-invalid"};
|
||||
const auto path = directory.Path() / "dynamic_log.txt";
|
||||
for (std::size_t index = 0U; index < mutations.size(); ++index) {
|
||||
SCOPED_TRACE(index);
|
||||
fesa::NewtonIterationLogWriter writer;
|
||||
ASSERT_TRUE(writer.Open(path).IsOk());
|
||||
ASSERT_TRUE(writer.Write(CompleteDynamicRecord()).IsOk());
|
||||
ASSERT_TRUE(writer.Flush().IsOk());
|
||||
const std::string prefix = ReadLogBytes(path);
|
||||
auto invalid = CompleteDynamicRecord();
|
||||
mutations[index](invalid);
|
||||
ExpectLogOutputFailure(writer.Write(invalid));
|
||||
ExpectLogOutputFailure(writer.Write(CompleteDynamicRecord()));
|
||||
ExpectLogOutputFailure(writer.Flush());
|
||||
ExpectLogOutputFailure(writer.Close());
|
||||
EXPECT_EQ(ReadLogBytes(path), prefix);
|
||||
}
|
||||
fesa::NewtonIterationLogWriter unopened;
|
||||
ExpectLogOutputFailure(unopened.Write(CompleteDynamicRecord()));
|
||||
}
|
||||
|
||||
} // namespace
|
||||
|
||||
Reference in New Issue
Block a user