Diwan, GC;
Moiola, A;
Spence, EA;
(2019)
Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?
Journal of Computational and Applied Mathematics
, 352
pp. 110-131.
10.1016/j.cam.2018.11.035.
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Abstract
A new, coercive formulation of the Helmholtz equation was introduced in [1]. In this paper we investigate h-version Galerkin discretisations of this formulation, and the iterative solution of the resulting linear systems. We find that the coercive formulation behaves similarly to the standard formulation in terms of the pollution effect (i.e. to maintain accuracy as k → ∞, h must decrease with k at the same rate as for the standard formulation). We prove k-explicit bounds on the number of GMRES iterations required to solve the linear system of the new formulation when it is preconditioned with a prescribed symmetric positive-definite matrix. Even though the number of iterations grows with k, these are the first such rigorous bounds on the number of GMRES iterations for a preconditioned formulation of the Helmholtz equation, where the preconditioner is a symmetric positive-definite matrix.
| Type: | Article |
|---|---|
| Title: | Can coercive formulations lead to fast and accurate solution of the Helmholtz equation? |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cam.2018.11.035 |
| Publisher version: | https://doi.org/10.1016/j.cam.2018.11.035 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Helmholtz equation, finite element method, coercive variational formulation, pollution effect, wavenumber-explicit analysis, GMRES |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10071583 |
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