An efficient preconditioner for adaptive Fast Multipole accelerated Boundary Element Methods to model time-harmonic 3D wave propagation - Archive ouverte HAL
Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2019

An efficient preconditioner for adaptive Fast Multipole accelerated Boundary Element Methods to model time-harmonic 3D wave propagation

Abstract

This paper presents an efficient algebraic preconditioner to speed up the convergence of Fast Multipole accelerated Boundary Element Methods (FM-BEMs) in the context of time-harmonic 3D wave propagation problems and in particular the case of highly non-uniform discretizations. Such configurations are produced by a recently-developed anisotropic mesh adaptation procedure that is independent of partial differential equation and integral equation. The new preconditioning methodology exploits a complement between fast BEMs by using two nested GMRES algorithms and rapid matrix-vector calculations. The fast inner iterations are evaluated by a coarse hierarchical matrix (H-matrix) representation of the BEM system. These inner iterations produce a preconditioner for FM-BEM solvers. It drastically reduces the number of outer GMRES iterations. Numerical experiments demonstrate significant speedups over non-preconditioned solvers for complex geometries and meshes specifically adapted to capture anisotropic features of a solution, including discontinuities arising from corners and edges.
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Dates and versions

hal-02113702 , version 1 (29-04-2019)

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Faisal Amlani, Stéphanie Chaillat, Adrien Loseille. An efficient preconditioner for adaptive Fast Multipole accelerated Boundary Element Methods to model time-harmonic 3D wave propagation. Computer Methods in Applied Mechanics and Engineering, 2019, 352 (1), pp.189-210. ⟨10.1016/j.cma.2019.04.026⟩. ⟨hal-02113702⟩
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