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- W2488501195 abstract "We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field 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 $krightarrow infty$ when the boundary of the obstacle is analytic and has strictly positive curvature. To our knowledge, this result is the first-ever 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 $k$-independent quasi-optimality of the Galerkin solutions as $k rightarrow infty$ when the obstacle is nontrapping." @default.
- W2488501195 created "2016-08-23" @default.
- W2488501195 creator A5007177846 @default.
- W2488501195 creator A5025891836 @default.
- W2488501195 creator A5083248653 @default.
- W2488501195 date "2016-08-03" @default.
- W2488501195 modified "2023-09-24" @default.
- W2488501195 title "Wavenumber-explicit analysis for the Helmholtz $h$-BEM: error estimates and iteration counts for the Dirichlet problem" @default.
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- W2488501195 hasPublicationYear "2016" @default.
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