FEM Study

Small C++ project implementing a 2D Galerkin finite element method for Poisson-type problems. Intended for experimenting with assembly strategies, matrix storage formats, and linear solvers.

Features

• Linear P1 triangular elements (stiffness matrix and load vector assembly)
• Dirichlet boundary conditions
• Gmsh .msh input, VTK output
• Multiple matrix backends: dense, banded, stack-based, sparse
• Linear solvers:
  • Direct: custom LDLᵀ, Eigen (SimplicialLDLT, SparseLU)
  • Iterative: Conjugate Gradient (CPU and OpenCL)

Code layout

• src/FEM*.cpp — FEM assembly and problem setup
• src/MatrixImpl/ — matrix formats and solvers
• src/time_series.cpp — simple benchmarking

Build notes

Solver backend is selected at compile time via: FEM_EIGEN_IMPL, FEM_CONJ_GRAD_IMPL, or FEM_NAIVE_IMPL.