Robust Boundary Element Domain Decomposition Solvers in Acoustics

Steinbach, Olaf; Windisch, Markus

doi:10.1007/978-3-642-11304-8_31

Cited by 11 publications

(4 citation statements)

References 5 publications

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“…Moreover, these methods are prone to spurious modes. A remedy for this consists in introducing Robintype conditions instead of classic transmission conditions [48]. Nonetheless, the model still requires the inclusion of Lagrange multipliers.…”

Section: Introductionmentioning

confidence: 99%

Multiple traces boundary integral formulation for Helmholtz transmission problems

Hiptmair

Jerez-Hanckes

2011

Adv Comput Math

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We 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 Calderón 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 H −1/2 -distributions over each associated interface. Through the use of interior Calderón 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.

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Section: Introductionmentioning

confidence: 99%

Multiple traces boundary integral formulation for Helmholtz transmission problems

Hiptmair

Jerez-Hanckes

2011

Adv Comput Math

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“…Non-overlapping surface integral equation domain decompostition method (SIE-DDM) has also been proposed by Peng and Lee [6], which relies on a DDM framework with generalized combined field integral equation (GCFIE). In addition, using different representation of the local Steklov-Poincare operators to formulate and analyze various boundary elements employed in local discretization schemes is presented by O.Steinbach [7].…”

Section: Introductionmentioning

confidence: 99%

Domain decomposition based integral equation method for electromagnetic scattering from dielectirc object

Jiang

Miao

et al. 2013

2013 IEEE Antennas and Propagation Society International Symposium (APSURSI)

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In this paper, a hybrid algorithm based on nonoverlapping domain decomposition method and surface Integral equation (SIE-DDM) is presented for dealing with time-harmonic electromagnetic (EM) problems of dielectric or composite object. The proposed method divides the composite object into homogeneous, non-overlapping sub-domains. Robin transmission condition is introduced to weakly enforce the continuity of tangential field across the touching-face between adjacent subdomains. Here, the electric and magnetic current combined-field integral equation (JMCFIE) is used for each sub-problem. The accuracy, efficiency, and meshing flexibility of the proposed method have been demonstrated by numerical results.

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“…Several approaches, such as Poggio‐Miller‐Chang‐Harrington‐Wu‐Tsai (PMCHWT) or the Boundary Element Tearing and Interconnecting (BETI) method , have been derived rather early for treating scattering by geometrically complex structures by means of boundary integral operators. Although the BETI method had already been applied to the Helmholtz equation by Steinbach and Windisch using local block‐diagonal preconditioning by operators of opposite order, which is closely related to the Calderón's preconditioning, most of the existing approaches did not lend themselves (at least as local solvers) to some of the most popular preconditioning techniques such as Calderón's preconditioner .…”

Section: Introductionmentioning

confidence: 99%

Quasi‐local multitrace boundary integral formulations

Claeys

2015

Numerical Methods Partial

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In the context of time harmonic wave scattering by piecewise homogeneous penetrable objects, we present a new variant of the multitrace boundary integral formulation, that differs from the local multitrace approach of (Jerez-Hanckes and Hiptmair, 2012) [13] by the presence of regularization terms involving boundary integral operators and localized at junctions i.e. points where at least three subdomains abut. We prove well-posedness and quasioptimal convergence of conforming Galerkin discretizations for this new formulation, and present numerical results.

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Robust Boundary Element Domain Decomposition Solvers in Acoustics

Cited by 11 publications

References 5 publications

Multiple traces boundary integral formulation for Helmholtz transmission problems

Multiple traces boundary integral formulation for Helmholtz transmission problems

Domain decomposition based integral equation method for electromagnetic scattering from dielectirc object

Quasi‐local multitrace boundary integral formulations

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