"My FEM" MATLAB Finite Element Solver

Overview

MyFEM is a comprehensive, MATLAB-based FEM solver, developed for ME C180 at UC Berkeley. It implements finite element analysis to solve structural and thermal boundary value problems.

Skills Demonstrated

• Finite Element Method/Analysis (FEM/FEA) – Implemented Galerkin’s Method FEM for structural and thermal problems from first principles.
• Numerical Linear Algebra – Constructed and solved large systems using MATLAB’s built-in solvers and custom optimized routines.
• Error Estimation & Adaptivity – Applied PMPE for error quantification and built an adaptive h-refinement algorithm for mesh convergence.
• MATLAB Programming – Developed modular, vectorized code optimized for readability and performance on low-spec hardware.

Software Engineering

The Finite Element Method (FEM) is a numerical technique for solving complex physical problems (differential equations). These include how heat spreads through a material or how a beam bends under load. For a class at UC Berkeley, I undertook the project of creating my own FEM code from scratch. This project demanded a rigorous, ground-up implementation of the finite element method, emphasizing both analytical understanding and practical execution. The result is a fully functional solver capable of handling nontrivial physical systems with minimal computational overhead. The code is modular, scalable, and runs on resource-constrained hardware without performance loss. It is designed to be runnable on weak hardware, including laptops and mobile phones.

The solver handles both Dirichlet and Neumann boundary conditions and is capable of:

• Discretizing 1D domains using linear, quadratic, and cubic shape functions
• Assembling global stiffness matrices and force vectors efficiently
• Solving systems using sparse linear algebra routines
• Performing error estimation via the Principle of Minimum Potential Energy (PMPE)
• Executing adaptive h-refinement based on residual error
• Remeshing non-uniform domains to improve convergence

Developing this solver required deep integration of mathematical theory with software engineering practices. Each feature from p-refinement, to adaptive meshing was implemented by hand, and validated through benchmark problems to confirm correctness and stability.

Core methods are based on The Basics, by Tarek Zohdi (SpringerLink), a rigorous treatment of finite element fundamentals.