UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?

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. Green open access

[thumbnail of Diwan_Can coercive formulations lead to fast and accurate solution of the Helmholtz equation_AAM.pdf]
Preview
Text
Diwan_Can coercive formulations lead to fast and accurate solution of the Helmholtz equation_AAM.pdf - Accepted Version

Download (2MB) | Preview

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
Downloads since deposit
72Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item