Performance of the multigrid method with time-stepping to solve 1D and 2D wave equations

Abstract

This work aims to discuss a proposed solution for wave equations that utilize discretization by means of the finite difference method, weighted by a parameter η, with sweeping done according to the time-stepping method. The multigrid method is employed to speed up the convergence in obtaining the solution of the system of equations resulting from the discretization. To validate the proposed model, the discretization errors, effective and apparent orders, convergence factor, orders of complexity, and the computational time were assessed. A comparison between the singlegrid and multigrid methods was carried out in order to determine the most advantageous one.

KEYWORDS:

• Complexity order
• finite difference method
• speed-up
• convergence
• wave equation
• multigrid

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brazil grant 88882.381810/2019-01 and Universidade Federal do Paraná grant 75.095.679/0001-49.