Multiple traces boundary integral formulation for Helmholtz transmission problems

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dc.contributor.authorHiptmair, R.
dc.contributor.authorJerez-Hanckes, C.
dc.date.accessioned2025-01-20T23:57:58Z
dc.date.available2025-01-20T23:57:58Z
dc.date.issued2012
dc.description.abstractWe present a novel boundary integral formulation of the Helmholtz transmission problem for bounded composite scatterers (that is, piecewise constant material parameters in "subdomains") that directly lends itself to operator preconditioning via Caldern projectors. The method relies on local traces on subdomains and weak enforcement of transmission conditions. The variational formulation is set in Cartesian products of standard Dirichlet and special Neumann trace spaces for which restriction and extension by zero are well defined. In particular, the Neumann trace spaces over each subdomain boundary are built as piecewise -distributions over each associated interface. Through the use of interior Caldern projectors, the problem is cast in variational Galerkin form with an operator matrix whose diagonal is composed of block boundary integral operators associated with the subdomains. We show existence and uniqueness of solutions based on an extension of Lions' projection lemma for non-closed subspaces. We also investigate asymptotic quasi-optimality of conforming boundary element Galerkin discretization. Numerical experiments in 2-D confirm the efficacy of the method and a performance matching that of another widely used boundary element discretization. They also demonstrate its amenability to different types of preconditioning.
dc.description.funderETH
dc.fuente.origenWOS
dc.identifier.doi10.1007/s10444-011-9194-3
dc.identifier.eissn1572-9044
dc.identifier.issn1019-7168
dc.identifier.urihttps://doi.org/10.1007/s10444-011-9194-3
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/95224
dc.identifier.wosidWOS:000304925800002
dc.issue.numero1
dc.language.isoen
dc.pagina.final91
dc.pagina.inicio39
dc.revistaAdvances in computational mathematics
dc.rightsacceso restringido
dc.subjectAcoustic scattering
dc.subjectBoundary integral equations
dc.subjectTrace spaces
dc.subjectCalderon projectors
dc.subjectBoundary elements
dc.titleMultiple traces boundary integral formulation for Helmholtz transmission problems
dc.typeartículo
dc.volumen37
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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