Programming of Finite Element Methods in MATLAB
Long Chen
TL;DR
This paper explains how to efficiently implement the linear finite element method for solving the Poisson equation in MATLAB, focusing on data structures, sparse matrices, and assembly processes.
Contribution
It provides a detailed guide on implementing finite element methods in MATLAB with an emphasis on efficient programming techniques.
Findings
Efficient assembly of finite element matrices in MATLAB.
Use of sparse matrices to optimize computations.
Practical implementation steps for solving Poisson equations.
Abstract
We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the assembling process. We pay special attention to an efficient programming style using sparse matrices in MATLAB.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Numerical Methods in Computational Mathematics · Numerical methods for differential equations