Fast and accurate multigrid solution of Poissons equation using diagonally oriented grids

1999/07/30 by A. J. Roberts, Roberts, A. J.
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.math/9907190

openalex publication_date 1999/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication between the levels of the multigrid. Numerical experiments solving Poisson's equation in the unit square and unit cube show simple versions of the proposed algorithms are up to twice as fast as correspondingly simple multigrid iterations on a conventional hierarchy of grids.

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