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Product algebras for Galerkin discretisations of boundary integral operators and their applications

Betcke, T; Scroggs, M; Smigaj, W; (2020) Product algebras for Galerkin discretisations of boundary integral operators and their applications. ACM Transactions on Mathematical Software , 46 (1) , Article 4. 10.1145/3368618. Green open access

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Abstract

Operator products occur naturally in a range of regularised boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp, we have implemented a complete operator algebra that depends on knowledge of the domain, range, and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible, while hiding the complexities of Galerkin discretisations. In this article, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems.

Type: Article
Title: Product algebras for Galerkin discretisations of boundary integral operators and their applications
Open access status: An open access version is available from UCL Discovery
DOI: 10.1145/3368618
Publisher version: https://doi.org/10.1145/3368618
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: Boundary integral equations, operator preconditioning, boundary element software
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10088519
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