Local strategies for improving the conditioning of the plane-wave Ultra-Weak Variational Formulation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:441

Article

Barucq, Helene^1,2  Bendali, Abderrahmane³  Diaz, Julien^1,2  Tordeux, Sebastien^1,2 

[1] INRIA, Makutu, Paris, France

[2] CNRS, E2S UPPA, UMR 5142, Paris, France

[3] Univ Toulouse, INSA Toulouse, IMT UMR CNRS 5219, 135 Ave Rangueil, F-31400 Toulouse, France

关键词: Helmholtz;    UWVF;    Plane waves;    SVD;    QR;   

DOI  :  10.1016/j.jcp.2021.110449

来源: Elsevier

【 摘 要 】

Element-wise techniques based on SVD or QR Decomposition completely get rid of the usual ill-conditioning inherent to the plane-wave discretizations of the Ultra-Weak Variational Formulation (UWVF) for the Helmholtz equation. Associated preconditioning strategies lead to very low condition numbers of the corresponding linear system matrices, without any limitation on the number of plane waves per element. In addition, some of these procedures have the advantage of considerably reducing the size of the final system to be solved without altering the accuracy of the numerical solution. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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