Investigation of efficiency of the higher-level multigrid methods for solving a large system of linear equations which arises from discretizing numerical schemes of 1D Poisson equation

Abstract

Multigrid Methods (MG) are extremely effective numerical techniques in solving a large system of linear equations associated with boundary value problems in various fields such as engineering, physics, and medicine etc. The references show that, in general, the order of computational complexity of multigrid methods is (𝑁) whereas classical linear system solver like Gauss-Seidel (GS) takes the order 𝑂(𝑁2). The objective of this research is to implement the multigrid algorithm using MATLAB software and to solve a large linear system of equations using the implemented algorithm to evaluate the convergence nature of MG.