An alternative extended linear system for boundary value problems on locally perturbed geometries

DOI10.1016/J.JCP.2021.110182arXiv2007.08571WikidataQ114163474 ScholiaQ114163474MaRDI QIDQ6345250

Publication date: 16 July 2020

Abstract: This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique for which the authors have constructed a fast direct solver. The key features of the work presented in this paper are that the fast direct solver is more efficient for the new extended linear system and that problems involving specialized quadrature for weakly singular kernels can be easily handled. Numerical results illustrate the improved performance of the fast direct solver for the new extended system when compared to the fast direct solver for the original extended system.

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Numerical methods for partial differential equations, boundary value problems (65N99)

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