MATLAB Finite Element Functions for Electromagnetic Field Simulation

This article presents MATLAB-implemented finite element functions containing core algorithmic components for basic finite element operations. These functions provide critical tools for simulating electromagnetic fields using finite element methods - a complex task that requires sophisticated numerical approaches. The finite element method serves as a numerical computation technique for solving differential equations, particularly vital in electromagnetics where accurate field simulation demands precise computational frameworks. These foundational functions incorporate essential finite element components including mesh generation algorithms (using Delaunay triangulation or advancing front methods), discretization procedures (through Galerkin weighted residual formulation), and linear system solvers (employing sparse matrix techniques like Cholesky decomposition or iterative methods). Key MATLAB functions implemented include element stiffness matrix computation using shape functions, boundary condition application through penalty methods or Lagrange multipliers, and post-processing routines for field visualization. Understanding these computational aspects—mesh generation principles, discretization techniques, and linear algebra solvers—proves essential for electromagnetic research, enabling researchers to better interpret field behaviors and achieve higher simulation accuracy through robust numerical implementations.