Introduction to the Finite Element Method in Electromagnetics with Source Code Examples

This document provides a comprehensive introduction to the Finite Element Method (FEM) applied to electromagnetic problems, accompanied by fully implemented source code. The codebase contains 4-5 practical FEM examples covering both 1D and 2D implementations, specifically designed for beginners. Each example demonstrates key FEM components including mesh generation using nodal discretization, implementation of shape functions for linear/quadratic elements, assembly of global stiffness matrices through element-wise integration, and boundary condition handling techniques. The finite element method serves as a fundamental computational tool for electromagnetic field analysis and device design, working by decomposing complex geometries into simpler finite elements where Maxwell's equations are solved locally. The provided code implementations establish a solid foundation in FEM workflow - from problem formulation and matrix assembly to numerical solution techniques - preparing learners for advanced electromagnetic simulations involving edge elements, vector formulations, and frequency-domain analysis.