feat(fem-and-beam-kernel): step 0 — quadrature-and-shape-functions

src/fesa/fem/gauss_rule.cpp

@@ -0,0 +1,33 @@
+#include <fesa/fem/gauss_rule.hpp>
+
+#include <array>
+#include <stdexcept>
+
+namespace fesa {
+
+namespace {
+
+constexpr std::array<GaussPoint1D, 1> order_one{{
+    {0.0, 2.0},
+}};
+
+constexpr double inverse_sqrt_three = 0.57735026918962576451;
+constexpr std::array<GaussPoint1D, 2> order_two{{
+    {-inverse_sqrt_three, 1.0},
+    {inverse_sqrt_three, 1.0},
+}};
+
+}  // namespace
+
+std::span<const GaussPoint1D> gauss_rule_1d(const int order) {
+    switch (order) {
+        case 1:
+            return order_one;
+        case 2:
+            return order_two;
+        default:
+            throw std::invalid_argument{"Gauss rule order must be 1 or 2."};
+    }
+}
+
+}  // namespace fesa

src/fesa/fem/line2_shape.cpp

@@ -0,0 +1,31 @@
+#include <fesa/fem/line2_shape.hpp>
+
+#include <cmath>
+#include <stdexcept>
+
+namespace fesa {
+
+std::array<double, 2> line2_shape(const double xi) {
+    return {0.5 * (1.0 - xi), 0.5 * (1.0 + xi)};
+}
+
+std::array<double, 2> line2_shape_derivative(const double) {
+    return {-0.5, 0.5};
+}
+
+double line2_jacobian(const double length) {
+    if (!std::isfinite(length) || length <= 0.0) {
+        throw std::invalid_argument{
+            "Line2 Jacobian requires a positive finite length."};
+    }
+
+    const double jacobian = length / 2.0;
+    if (jacobian == 0.0) {
+        throw std::invalid_argument{
+            "Line2 Jacobian must be representable as a positive double."};
+    }
+
+    return jacobian;
+}
+
+}  // namespace fesa