Application of multigrid methods for solving systems of linear algebraic equations of large dimension in the context of model differential equations

Abstract The geometric multigrid method has been implemented using the V-cycle for solving the high-dimensional linear algebraic equation systems that appear when applying the finite element and finite difference methods for the problems of mathematical physics. The results of the convergence comparison between the classical iterative methods (Jacobi, Gauss-Seidel or the conjugate gradient method) and the implemented geometric multigrid method have been obtained.