A Comparison of SOR, ADI and Multigrid Methods for Solving Partial Differential Equations

TL;DR

This paper compares various numerical methods like Jacobi, Gauss-Seidel, SOR, ADI, and Multigrid for solving the 2D Laplace equation, highlighting their efficiencies and differences through a FORTRAN implementation.

Contribution

It provides a detailed comparison of multiple numerical techniques for solving Laplace equations, including implementation and performance analysis.

Findings

Multigrid method shows faster convergence.

SOR method improves over Gauss-Seidel.

Method performance varies with problem size.

Abstract

This article presents several numerical techniques for solving Laplace equation. A numerical FORTRAN solver is developed to solve the 2D laplace equation. The numerical approaches implemented in the solver include Jacobi, Gauss-Siedel, Successive Over Relaxation, Alternating Direct Implicit and Multigrid methods. Detailed comparison between different numerical methods is presented and discussed