QUASI-LOCAL AND FREQUENCY-ROBUST PRECONDITIONERS FOR THE HELMHOLTZ FIRST-KIND INTEGRAL EQUATIONS ON THE DISK

被引:0
作者
Alouges, Francois [1 ]
Averseng, Martin [2 ]
机构
[1] ENS Paris Saclay, Dept Math, Ctr Borelli, F-91190 Gif sur Yvette, France
[2] Univ Angers, Lab Angevin Rech Math, 2 Bd Lavoisier, F-49000 Angers, France
关键词
Boundary element methods; preconditioning; singularities in PDEs; BOUNDARY-ELEMENT METHOD; ALGORITHM; MATRICES; GMRES;
D O I
10.1051/m2an/2023105
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We propose preconditioners for the Helmholtz scattering problems by a planar, disk-shaped screen in R-3. Those preconditioners are approximations of the square-roots of some partial differential operators acting on the screen. Their matrix-vector products involve only a few sparse system resolu- tions and can thus be evaluated cheaply in the context of iterative methods. For the Laplace equation (i.e. for the wavenumber k = 0) with Dirichlet condition on the disk and on regular meshes, we prove that the preconditioned linear system has a bounded condition number uniformly in the mesh size. We further provide numerical evidence indicating that the preconditioners also perform well for large values of k and on locally refined meshes.
引用
收藏
页码:793 / 831
页数:39
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