A simplified technique for the efficient and highly accurate discretization of boundary integral equations in 2D on domains with corners

Gillman, Adrianna; Hao, Sijia; Martinsson, Per-Gunnar

doi:10.1016/j.jcp.2013.08.049

Cited by 13 publications

(16 citation statements)

References 12 publications

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“…Intense and costly mesh refinement is then needed for resolution, which may lead to the loss of stability. See [14] for a review of recently developed numerical techniques to deal with this problem.…”

Section: Recursively Compressed Inverse Preconditioningmentioning

confidence: 99%

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Determination of normalized electric eigenfields in microwave cavities with sharp edges

Helsing

2016

Journal of Computational Physics

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Section: Recursively Compressed Inverse Preconditioningmentioning

confidence: 99%

“…RCIP is one of the techniques discussed in [14]. It can be viewed as a general method to enhance the performance of panel-based Nyström discretization schemes.…”

Section: Recursively Compressed Inverse Preconditioningmentioning

confidence: 99%

Determination of normalized electric eigenfields in microwave cavities with sharp edges

Helsing

2016

Journal of Computational Physics

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“…It appears conceptually straight-forward to use the techniques of [1,14] to generalize the method presented to handle scatterers with edges (generated by "corners" in the generating curve). The idea is to use local refinement to resolve the singular behavior of solutions near the corner, and then eliminate the added "superfluous" degrees of freedom added by the refinement via a local compression technique, see [6].…”

Section: Discussionmentioning

confidence: 99%

An efficient and highly accurate solver for multi-body acoustic scattering problems involving rotationally symmetric scatterers

Hao

Martinsson

Young

2015

Computers & Mathematics with Applications

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a b s t r a c tA numerical method for solving the equations modeling acoustic scattering in three dimensions is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries involving cavities, solutions accurate to seven digits or better were obtained. The method relies on a Boundary Integral Equation formulation of the scattering problem, discretized using a high-order accurate Nyström method. A hybrid iterative/direct solver is used in which a local scattering matrix for each body is computed, and then GMRES, accelerated by the Fast Multipole Method, is used to handle reflections between the scatterers. The main limitation of the method described is that it currently applies only to scattering bodies that are rotationally symmetric.

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“…Note that this refinement procedure introduces a superfluous amount of points near the junctions. The extra points can be eliminated via compression techniques presented in [1,6,7,5,3]. Since the focus of this paper is on the performance of the integral formulation, no compression techniques are utilized in the numerical experiments in section 4.…”

Section: Discretizationmentioning

confidence: 99%

An integral equation technique for scattering problems with mixed boundary conditions

Gillman

2016

Adv Comput Math

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This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a result, Calderón identities can be utilized to avoid the use of hypersingular integral operators. More importantly, the formulation avoids spurious resonances. Numerical results illustrate the performance of the proposed solution technique.

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A simplified technique for the efficient and highly accurate discretization of boundary integral equations in 2D on domains with corners

Cited by 13 publications

References 12 publications

Determination of normalized electric eigenfields in microwave cavities with sharp edges

Determination of normalized electric eigenfields in microwave cavities with sharp edges

An efficient and highly accurate solver for multi-body acoustic scattering problems involving rotationally symmetric scatterers

An integral equation technique for scattering problems with mixed boundary conditions

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