A Second-Kind Galerkin Boundary Element Method for Scattering at Composite Objects

Xavier Claeys (1, 2) , Ralf Hiptmair (3) , Elke Spindler (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
3 SAM - Seminar of Applied Mathematics [Zürich]

We consider the scattering of time-harmonic acoustic waves at objects composed of several homogeneous parts with different material properties. In [X. Claeys, A single trace integral formulation of the second kind for acoustic scattering, Report 2011-14, SAM, ETH Zürich] a novel second-kind boundary integral formulation for this scattering problem was proposed. We recast it into a variational problem set in L2 and investigate its Galerkin boundary element discretization from a theoretical and algorithmic point of view. Empiric studies demonstrate the competitive accuracy and superior conditioning of the new approach compared to a widely used Galerkin boundary element approach based on a first-kind boundary integral formulation.

Mots clés: Galerkin boundary element methods; second-kind boundary integral equations; Acoustic scattering

Domaines: Analyse numérique [math.NA]

Xavier Claeys, Ralf Hiptmair, Elke Spindler. A Second-Kind Galerkin Boundary Element Method for Scattering at Composite Objects. BIT Numerical Mathematics, 2015, 55 (1), pp.33-57. ⟨10.1007/s10543-014-0496-y⟩. ⟨hal-00909835⟩