Open Access

ARTICLE

Subdomain method in time with waveform relaxation in space applied to the wave equation combined with the multigrid method

Maicon Felipe Malacarne¹, Marcio Augusto Villela Pinto², Sebastião Romero Franco³

1 Universidade Federal do Paraná, Faculdade Biopark, Brazil
2 Department of Mechanical Engineering - Federal University of Parana
3 Department of Mathematics - State University of Centro-Oeste - UNICENTRO

* Corresponding Authors: Maicon Felipe Malacarne (), Marcio Augusto Villela Pinto (), Sebastião Romero Franco ()

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 2022, 38(4), 1-22. https://doi.org/10.23967/j.rimni.2022.11.001

Accepted 27 October 2022; Issue published 08 November 2022

Abstract

This work aims to evaluate a parallelizable approximate solution model for the wave equation. For that, we used the temporal sweep known as the Waveform Relaxation method to guarantee the parallelization in space. However, this technique has limitations for this class of problems. Therefore, we proposed the combination of the Subdomain method in a non-conventional way in time with the Multigrid method, intending to reduce computational time and improve the convergence factors. In this work, we presented the mathematical analysis of the stability of the discretization model, which uses the Central Finite Difference method with weighting at each time step. As an application of the proposed method, in addition to a problem with a known analytical solution, we solved a wave propagation problem with reflection and phase inversion.

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Keywords

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