Directional H^(2) Compression Algorithm: Optimisations and Application to a Discontinuous Galerkin BEM for the Helmholtz Equation

作     者：Nadir-Alexandre Messaï Sebastien Pernet Abdesselam Bouguerra 

作者机构：ONERA/DTISUniversitéfédérale de Toulouse F-31000 Toulouse France Laboratoire de Physique de la Matière et du Rayonnement(LPMR)Département de Sciences de la MatièreUniversitéde Souk-AhrasBP 155341000 Souk-AhrasAlgeria 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2022年第31卷第5期

页      面：1585-1635页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 

主　　题：Integral equation boundary element method Helmholtz equation discontinuous Galerkin directional H^(2)-matrix low-rank approximation all frequency compression algorithm 

摘      要：This study aimed to specialise a directional H^(2)(DH^(2))compression to matrices arising from the discontinuous Galerkin(DG)discretisation of the hypersingular equation in acoustics.The significantfinding is an algorithm that takes a DG stiffness matrix andfinds a near-optimal DH^(2) 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 DH^(2) 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.