The complex-scaled half-space matching method

Bonnet-Ben Dhia, A.-S., Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Fliss, S., Hazard, C., Perfekt, K.-M. and Tjandrawidjaja, Y. (2022) The complex-scaled half-space matching method. SIAM Journal on Mathematical Analysis (SIMA), 54 (1). pp. 512-557. ISSN 0036-1410 doi: 10.1137/20M1387122

Abstract/Summary

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to {Perfectly Matched Layers (PML)} or other artificial boundary conditions. Based on half-plane representations for the solution, the scattering problem is rewritten as a system of integral equations in which the unknowns are restrictions of the solution to the boundaries of a finite number of overlapping half-planes contained in the domain: this integral equation system is coupled to a standard finite element discretisation localised around the scatterer. While satisfactory numerical results have been obtained for real wavenumbers, wellposedness and equivalence to the original scattering problem have been established only for complex wavenumbers. In the present paper, by combining the HSM framework with a complex-scaling technique, we provide a new formulation for real wavenumbers which is provably well-posed and has the attraction for computation that the complex-scaled solutions of the integral equation system decay exponentially at infinity. The analysis requires the study of double-layer potential integral operators on intersecting infinite lines, and their analytic continuations. The effectiveness of the method is validated by preliminary numerical results.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/100188
Identification Number/DOI	10.1137/20M1387122
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Society for Industrial and Applied Mathematics
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