Finite Element Method Implementation Using MATLAB

In this article, we employ a highly efficient computational approach – the Finite Element Method (FEM), which utilizes numerical computation techniques through computer implementation to effectively solve diverse engineering problems. The FEM algorithm works by decomposing complex problems into smaller subdomains (finite elements), solving each element individually, and then assembling the solutions to obtain the complete problem resolution. Our implementation leverages MATLAB's powerful computational environment, which provides essential toolboxes and built-in functions for matrix operations, linear algebra solvers, and visualization tools that enhance simulation accuracy. The code structure typically involves mesh generation using functions like `pdegeom` for geometry definition, element stiffness matrix assembly through Gaussian quadrature integration, and solving linear systems with backslash operators or specialized solvers like `pcg` for large sparse systems. Through this MATLAB-based FEM implementation, we achieved excellent results that provide deeper insights into problem behavior and facilitate more effective engineering solutions.