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Well-Posedness Analysis and Numerics of Boundary-Domain Integral Equation Systems Equivalent to the Robin Problem for the Helmholtz Equation With Variable Coefficients in Lipschitz Domains

Authors

FRESNEDA PORTILLO, CARLOS, Caruso, Nahuel D.

External publication

No

Means

Math. Meth. Appl. Sci.

Scope

Article

Nature

Científica

JCR Quartile

✓

SJR Quartile

✗

Publication date

30/07/2025

ISI

001485931700001

DOI

10.1002/mma.10965

Abstract

Given the interior Robin boundary value problem (BVP) for the Helmholtz equation with variable coefficients, we use an appropriate parametrix to derive two boundary-domain integral equation systems (BDIES) equivalent to the original Robin BVP in Lipschitz domains. One then can choose which BDIES might be more convenient to be solved numerically. Main results of the paper concern the equivalence between the BDIE systems obtained and the original BVP, as well as well-posedness of the BDIES, which does not contain hypersingular operators. The last sections of the paper are devoted to confirm the theoretical results with various numerical experiments in 2D.

Keywords

boundary-domain integral equations; Helmholtz equation; parametrix; Robin boundary value problem