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Directional H2 Compression Algorithm: Optimisations and Application to a Discontinuous Galerkin BEM for the Helmholtz Equation

Directional $\mathcal{H}^2$ Compression Algorithm: Optimisations and Application to a Discontinuous Galerkin BEM for the Helmholtz Equation

Year:    2022

Author:    Nadir-Alexandre Messaï, Sebastien Pernet, Abdesselam Bouguerra

Communications in Computational Physics, Vol. 31 (2022), Iss. 5 : pp. 1585–1635

Abstract

This study aimed to specialise a directional H2(DH2) compression to matrices arising from the discontinuous Galerkin (DG) discretisation of the hypersingular equation in acoustics. The significant finding is an algorithm that takes a DG stiffness matrix and finds a near-optimal DH2 approximation for low and high-frequency problems. We introduced the necessary special optimisations to make this algorithm more efficient in the case of a DG stiffness matrix. Moreover, an automatic parameter tuning strategy makes it easy to use and versatile. Numerical comparisons with a classical Boundary Element Method (BEM) show that a DG scheme combined with a DH2 gives better computational efficiency than a classical BEM in the case of high-order finite elements and hp heterogeneous meshes. The results indicate that DG is suitable for an auto-adaptive context in integral equations.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2021-0241

Communications in Computational Physics, Vol. 31 (2022), Iss. 5 : pp. 1585–1635

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    51

Keywords:    Integral equation boundary element method Helmholtz equation discontinuous Galerkin directional H2-matrix low-rank approximation all frequency compression algorithm.

Author Details

Nadir-Alexandre Messaï Email

Sebastien Pernet Email

Abdesselam Bouguerra Email