Substructuring based FEM-BEM coupling for Helmholtz problems - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Substructuring based FEM-BEM coupling for Helmholtz problems

Résumé

This talk concerns the solution of the Helmholtz equation in a medium composed of a bounded heterogeneous domain and an unbounded homogeneous one. Such problems can be expressed using classical FEM-BEM coupling techniques. We solve these coupled formulations using iterative solvers based on substructuring Domain Decomposition Methods (DDM), and aim to develop a convergence theory, with fast and guaranteed convergence. A recent article of Xavier Claeys proposed a substructuring Optimized Schwarz Method, with a nonlocal exchange operator, for Helmholtz problems on a bounded domain with classical conditions on its boundary (Dirichlet, Neumann, Robin). The variational formulation of the problem can be written as a bilinear application associated with the volume and another with the surface, for which, under certain sufficient assumptions, convergence of the DDM strategy is guaranteed. In this presentation we show how some specific FEM-BEM coupling methods fit, or not, the previous framework, in which we consider Boundary Integral Equations (BIEs) instead of classical boundary conditions. In particular, we prove that the symmetric Costabel coupling satisfies the framework assumptions, implying that the convergence is guaranteed.
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Dates et versions

hal-04701091 , version 1 (18-09-2024)

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Antonin Boisneault, Marcella Bonazzoli, Xavier Claeys, Pierre Marchand. Substructuring based FEM-BEM coupling for Helmholtz problems. WAVES 2024 - 16th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jun 2024, Berlin, Germany. ⟨10.17617/3.MBE4AA⟩. ⟨hal-04701091⟩
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