A Matlab Tutorial for Diffusion-Convection-Reaction Equations using DGFEM
Murat Uzunca, B\"ulent Karas\"ozen
TL;DR
This paper provides MATLAB routines utilizing the discontinuous Galerkin finite element method to efficiently solve steady-state diffusion-convection-reaction equations, emphasizing code optimization through vectorization and sparse matrices.
Contribution
It introduces a set of MATLAB routines implementing DGFEM with optimized sparse matrix operations for solving complex PDEs.
Findings
Efficient MATLAB implementation of DGFEM for PDEs.
Use of vectorization and sparse matrices enhances computational performance.
Applicable to steady-state diffusion-convection-reaction problems.
Abstract
We present a collection of MATLAB routines using discontinuous Galerkin finite elements method (DGFEM) for solving steady-state diffusion-convection-reaction equations. The code employs the sparse matrix facilities of MATLAB with "vectorization" and uses multiple matrix multiplications {\it "MULTIPROD"} to increase the efficiency of the program.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Differential Equations and Numerical Methods · Numerical methods for differential equations