Abstract
We consider solving the exterior Dirichlet problem for the Helmholtz equation with the hversion of the boundary element method (BEM) using the standard secondkind combinedfield integral equations. We prove a new, sharp bound on how the number of GMRES iterations must grow with the wavenumber k to have the error in the iterative solution bounded independently of k as k→∞ when the boundary of the obstacle is analytic and has strictly positive curvature. To our knowledge, this result is the firstever sharp bound on how the number of GMRES iterations depends on the wavenumber for an integral equation used to solve a scattering problem. We also prove new bounds on how h must decrease with k to maintain kindependent quasioptimality of the Galerkin solutions as k→∞ when the obstacle is nontrapping.
Original language  English 

Pages (fromto)  329357 
Number of pages  29 
Journal  Numerische Mathematik 
Volume  142 
Issue number  2 
DOIs  
Publication status  Published  1 Jun 2019 
ASJC Scopus subject areas
 Computational Mathematics
 Applied Mathematics
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Euan Spence
 Department of Mathematical Sciences  Professor
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching
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High Performance Computing (HPC) Facility
Steven Chapman (Manager)
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