Fast Parallel Solver for the Space-time IgA-DG Discretization of the Diffusion Equation

Pietro Benedusi; Paola Ferrari; Carlo Garoni; Rolf Krause; Stefano Serra-Capizzano

doi:10.1007/s10915-021-01567-z

Fast Parallel Solver for the Space-time IgA-DG Discretization of the Diffusion Equation

Pietro Benedusi, Paola Ferrari, Carlo Garoni^*, Rolf Krause, Stefano Serra-Capizzano

^*Corresponding author for this work

Applied Mathematics and Computational Science

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We consider the space-time discretization of the diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines a preconditioned GMRES with a standard multigrid acting only in space. The performance of the proposed solver is illustrated through numerical experiments, which show its competitiveness in terms of iteration count, run-time and parallel scaling.

Original language	English (US)
Article number	20
Journal	Journal of Scientific Computing
Volume	89
Issue number	1
DOIs	https://doi.org/10.1007/s10915-021-01567-z
State	Published - Oct 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).

Keywords

Diffusion equation
Discontinuous Galerkin
Isogeometric analysis
Multigrid
Parallel solver
Preconditioned GMRES
Spectral distribution

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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title = "Fast Parallel Solver for the Space-time IgA-DG Discretization of the Diffusion Equation",

abstract = "We consider the space-time discretization of the diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines a preconditioned GMRES with a standard multigrid acting only in space. The performance of the proposed solver is illustrated through numerical experiments, which show its competitiveness in terms of iteration count, run-time and parallel scaling.",

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AU - Benedusi, Pietro

AU - Ferrari, Paola

AU - Garoni, Carlo

AU - Krause, Rolf

AU - Serra-Capizzano, Stefano

PY - 2021/10

Y1 - 2021/10

N2 - We consider the space-time discretization of the diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines a preconditioned GMRES with a standard multigrid acting only in space. The performance of the proposed solver is illustrated through numerical experiments, which show its competitiveness in terms of iteration count, run-time and parallel scaling.

AB - We consider the space-time discretization of the diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines a preconditioned GMRES with a standard multigrid acting only in space. The performance of the proposed solver is illustrated through numerical experiments, which show its competitiveness in terms of iteration count, run-time and parallel scaling.

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KW - Discontinuous Galerkin

KW - Isogeometric analysis

KW - Multigrid

KW - Parallel solver

KW - Preconditioned GMRES

KW - Spectral distribution

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ER -

Fast Parallel Solver for the Space-time IgA-DG Discretization of the Diffusion Equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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