Quotient-space boundary element methods for scattering at complex screens
| Autor: | Ralf Hiptmair, Xavier Claeys, Lorenzo Giacomel, Carolina Urzúa-Torres |
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| Přispěvatelé: | Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Algorithms and parallel tools for integrated numerical simulations (ALPINES), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), European Organization for Nuclear Research (CERN), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), Delft University of Technology (TU Delft), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Helmholtz equation
Discretization Complex screens Computer Networks and Communications Applied Mathematics Galerkin boundary element method 010102 general mathematics Mathematical analysis Quotient space boundary element method 010103 numerical & computational mathematics Krylov subspace Quotient space (linear algebra) 01 natural sciences Generalized minimal residual method Quotient spaceboundary element method Computational Mathematics Kernel (algebra) [MATH]Mathematics [math] 0101 mathematics Galerkin method Boundary element method Software Mathematics |
| Zdroj: | BIT Numerical Mathematics, 61 (4) BIT Numerical Mathematics BIT Numerical Mathematics, 2021, ⟨10.1007/s10543-021-00859-y⟩ BIT Numerical Mathematics, Springer Verlag, 2021, ⟨10.1007/s10543-021-00859-y⟩ Bit (Lisse): numerical mathematics, 61(4) |
| ISSN: | 0006-3835 1572-9125 |
| DOI: | 10.1007/s10543-021-00859-y⟩ |
| Popis: | A complex screen is an arrangement of panels that may not be even locally orientable because of junction lines. A comprehensive trace space framework for first-kind variational boundary integral equations on complex screens has been established in Claeys and Hiptmair (Integr Equ Oper Theory 77:167–197, 2013. https://doi.org/10.1007/s00020-013-2085-x) for the Helmholtz equation, and in Claeys and Hiptmair (Integr Equ Oper Theory 84:33–68, 2016. https://doi.org/10.1007/s00020-015-2242-5) for Maxwell’s equations in frequency domain. The gist is a quotient space perspective that allows to make sense of jumps of traces as factor spaces of multi-trace spaces modulo single-trace spaces without relying on orientation. This paves the way for formulating first-kind boundary integral equations in weak form posed on energy trace spaces. In this article we extend that idea to the Galerkin boundary element (BE) discretization of first-kind boundary integral equations. Instead of trying to approximate jumps directly, the new quotient space boundary element method employs a Galerkin BE approach in multi-trace boundary element spaces. This spawns discrete boundary integral equations with large null spaces comprised of single-trace functions. Yet, since the right-hand-sides of the linear systems of equations are consistent, Krylov subspace iterative solvers like GMRES are not affected by the presence of a kernel and still converge to a solution. This is strikingly confirmed by numerical tests. BIT Numerical Mathematics, 61 (4) ISSN:0006-3835 ISSN:1572-9125 |
| Databáze: | OpenAIRE |
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