Mortar Boundary Elements

Healey, M.; Heuer, Norbert

doi:10.1137/090748342

Cited by 13 publications

(21 citation statements)

References 25 publications

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“…The following is a well-established result, see, e.g., [27]. 9 Proposition 4. Denote by r (k) := P −1 (f − Cx (k) ) the residual of the k-th preconditioned MINRES iteration x (k) with inner product · , · P .…”

Section: Preconditioningmentioning

confidence: 85%

“…The first paper on non-conforming BEM considers a Lagrangian multiplier to deal with the homogeneous boundary condition on open surfaces [8]. This technique was extended in [9] to domain decomposition approximations, and is usually referred to as mortar method. In this paper we study preconditioners for the mortar BEM presented in [9].…”

Section: Introductionmentioning

confidence: 99%

“…This technique was extended in [9] to domain decomposition approximations, and is usually referred to as mortar method. In this paper we study preconditioners for the mortar BEM presented in [9]. These are the first results on preconditioning techniques for linear systems stemming from non-conforming boundary elements.…”

Section: Introductionmentioning

confidence: 99%

“…A priori error analysis for domain-oriented non-conforming boundary elements yields quasi-optimal error estimates which are perturbed by (poly-) logarithmic terms depending on the mesh size, see [3,8,9]. These perturbations appear due to the non-existence of a welldefined trace operator in the energy space of hypersingular operators.…”

Section: Introductionmentioning

confidence: 99%

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A wirebasket preconditioner for the mortar boundary element method

Führer

Heuer

2017

Adv Comput Math

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We present and analyze a preconditioner of the additive Schwarz type for the mortar boundary element method. As a basic splitting, on each subdomain we separate the degrees of freedom related to its boundary from the inner degrees of freedom. The corresponding wirebasket-type space decomposition is stable up to logarithmic terms. For the blocks that correspond to the inner degrees of freedom standard preconditioners for the hypersingular integral operator on open boundaries can be used. For the boundary and interface parts as well as the Lagrangian multiplier space, simple diagonal preconditioners are optimal. Our technique applies to quasi-uniform and non-uniform meshes of shaperegular elements. Numerical experiments on triangular and quadrilateral meshes confirm theoretical bounds for condition and MINRES iteration numbers.

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Section: Preconditioningmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A wirebasket preconditioner for the mortar boundary element method

Führer

Heuer

2017

Adv Comput Math

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“…Recently, a few formulations that impose solution constraints for some low-order discretizations have been advanced. Both a Lagrange multiplier and a penalty (Nitsche-type) method were developed in [9], [10] for a provably elliptic hypersingular integral equation associated with the Laplacian. Both of these approaches were extended without proof to three dimensional electromagnetic scattering problems in a penalty method for the three dimensional EFIE and MFIE [11] and a mortar element approach for the EFIE [12].…”

Section: Introductionmentioning

confidence: 99%

An Interior Penalty Method for the Generalized Method of Moments

Dault

Shanker

2015

IEEE Trans. Antennas Propagat.

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The Generalized Method of Moments is a technique to discretize integral equations that permits integration of different types of basis functions as well as different geometric descriptions using a partition of unity framework. While accuracy and efficacy of the method have been demonstrated, the integration quadratures required to compute the inner-products are often high as they have to respect spatial variation of the integrand. To overcome this problem, we introduce an interior penalty function method within the GMM framework. The penalty formulation yields solutions that are smooth and accurate both in surface currents and fields with significantly lower numerical quadrature orders than would be required for the uncompensated operator. To demonstrate and analyze the method, we conduct an analytical and numerical investigation of the properties of the penalty method applied to the 2D TE z Electric Field Integral Equation operator.

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A posteriori error analysis for a boundary element method with nonconforming domain decomposition

Domínguez

Heuer

2013

Numerical Methods Partial

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We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a nonconforming domain decomposition method based on the Nitsche technique. Assuming a saturation property, we establish quasireliability and efficiency of the error estimator in comparison with the error in a natural (nonconforming) norm. Numerical experiments with uniform and adaptively refined meshes confirm our theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 947–963, 2014

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Mortar Boundary Elements

Cited by 13 publications

References 25 publications

A wirebasket preconditioner for the mortar boundary element method

A wirebasket preconditioner for the mortar boundary element method

An Interior Penalty Method for the Generalized Method of Moments

A posteriori error analysis for a boundary element method with nonconforming domain decomposition

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