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+---
+type: concept
+title: "Midas NFX Equation Solvers and Eigen Extraction"
+created: 2026-06-02
+updated: 2026-06-02
+address: c-000177
+aliases:
+  - NFX equation solvers
+  - NFX eigen extraction
+tags:
+  - concept
+  - finite-element-method
+  - midas-nfx
+  - solvers
+  - eigenproblem
+status: current
+related:
+  - "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
+  - "[[midas NFX]]"
+  - "[[Static Equilibrium Equation Solvers]]"
+  - "[[Finite Element Eigenproblem Solvers]]"
+  - "[[Midas NFX Linear Dynamics and Buckling Analyses]]"
+sources:
+  - "[[Midas-NFX-Analysis-Manual|Midas NFX Analysis Manual]]"
+---
+
+# Midas NFX Equation Solvers and Eigen Extraction
+
+## Definition
+
+NFX equation solvers are the linear algebra back end used across static, eigenvalue, dynamic, and nonlinear analyses. The manual frames the basic linear problem as `K u = p` and the modal/buckling eigenproblem as `K phi_i - lambda_i B phi_i = 0`.
+
+## Linear Equation Solvers
+
+The source distinguishes dense direct solution, sparse multifrontal direct solution, out-of-core solution, GPU-assisted real matrix decomposition, and iterative solution. It states that direct solvers are generally robust but memory-intensive, while iterative solvers reduce memory demand but require preconditioning and can struggle with structural matrix characteristics.
+
+## Automatic Solver Selection
+
+NFX can select a solver by model size and available memory. The manual describes small problems going to dense or direct strategies, medium problems to multifrontal direct solution, and very large problems to AMG iterative solution when appropriate.
+
+## Eigen Extraction
+
+For normal modes and linear buckling, the manual connects solver choice to eigen extraction. Lanczos iteration is used with the multifrontal solver and is suited to large problems, while direct matrix methods are positioned for smaller tests. The source also emphasizes eigenvalue range/count settings, missing-eigenvalue checks, mode normalization, generalized mass/stiffness, orthogonality loss, and residual error measures.
+
+## Solver Development Use
+
+For a custom solver, this page defines verification targets beyond `K u = f`: sparse ordering, matrix factorization strategy, preconditioner policy, eigenvector normalization, modal mass checks, orthogonality checks, and residual norms should be part of the harness.
+
+## Connections
+
+- [[Static Equilibrium Equation Solvers]] gives the generic static solver context.
+- [[Finite Element Eigenproblem Solvers]] gives the shared modal and buckling eigenproblem context.
+- [[Midas FEA Nonlinear Solution Algorithms]] and [[Midas Civil Dynamic and Seismic Analysis]] are sibling MIDAS solver references.