Adaptive time domain boundary element methods with engineering applications

Gimperlein, Heiko; Maischak, Matthias; Stephan, Ernst P.

doi:10.1216/jie-2017-29-1-75

Cited by 20 publications

(28 citation statements)

References 34 publications

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“…as shown for the single layer potential in [8,10,11]. Because in practical computations we set σ = 0, we derive the estimate on finite time intervals [0, T ], but as in these sources also R + could be considered.…”

Section: An a Posteriori Error Estimatementioning

confidence: 99%

“…The density is plotted in snapshots at the time steps 100, 200 and 300 in Figure 5.10 (for the Dirichlet problem). See [2,8] for similar density profiles for the Neumann problem. Figure 5.8 shows the resulting sound pressure in the point (2.8m, 0, 1.0m).…”

Section: Acoustic Boundary Conditions In a Half-spacementioning

confidence: 99%

“…Also, fast collocation methods have been developed in the engineering literature [21]. Some recent work around space-time adaptive methods and applications is surveyed in [8]. A detailed exposition of the mathematical background of time domain integral equations and their discretizations is available in the lecture notes by Sayas [18].…”

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confidence: 99%

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Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems

Gimperlein¹,

Oezdemir

Stephan³

2018

JCM

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We investigate time domain boundary element methods for the wave equation in R 3 , with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approximations in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations obtained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.Mathematics subject classification: 65N38, 65R20, 74J05.

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Section: An a Posteriori Error Estimatementioning

confidence: 99%

Section: Acoustic Boundary Conditions In a Half-spacementioning

confidence: 99%

See 1 more Smart Citation

Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems

Gimperlein¹,

Oezdemir

Stephan³

2018

JCM

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“…Using [46], an analogous expansion to (20) also holds in this curved geometry, with the same leading singular term…”

Section: Singularities For Circular Screens and Approximationmentioning

confidence: 95%

“…The singular expansion for the inhomogeneous wave equation in (21) in R + t × K x implies an expansion for inhomogeneous boundary conditions in (20). The argument is as for elliptic problems [45,Section 5]: For Dirichlet conditions u| Γ = g on R + t ×∂K, we choose an extension…”

Section: Further Information Can Be Obtained By Combining the Convolumentioning

confidence: 99%

hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

Gimperlein

Özdemir

Stark

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R 3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.This article initiates the study of high-order boundary elements in the time domain. For elliptic problems, p-and hp-versions of the finite element method give rise to fast approximations of both smooth solutions and geometric singularities. These methods converge to the solution by increasing the polynomial degree p of the elements, possibly in combination with reducing the mesh size h of the quasi-uniform mesh. They were first investigated in the group of Babuska [3,4,17,18]. See [49] for a comprehensive analysis for 2d problems.The analogous p-and hp-versions of the boundary element method go back to [2,53,54]. More recent optimal convergence results for boundary elements on screens and polyhedral surfaces covering 3d problems have been obtained, for example, in [9,10,11,12,13].Boundary element methods for time dependent problems have recently become of interest [48]. In this article we introduce a space-time hp-version of the time domain boundary element method for the wave equation with non-homogeneous Dirichlet or Neumann boundary conditions.

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Space‐time stochastic Galerkin boundary elements for acoustic scattering problems

Gimperlein,

Meyer,

Özdemir

2024

Numerical Meth Engineering

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SummaryAcoustic emission or scattering problems naturally involve uncertainties about the sound sources or boundary conditions. This article initiates the study of time domain boundary elements for such stochastic boundary problems for the acoustic wave equation. We present a space‐time stochastic Galerkin boundary element method which is applied to sound‐hard, sound‐soft and absorbing scatterers. Uncertainties in both the sources and the boundary conditions are considered using a polynomial chaos expansion. The numerical experiments illustrate the performance and convergence of the proposed method in model problems and present an application to a problem from traffic noise.

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Adaptive time domain boundary element methods with engineering applications

Cited by 20 publications

References 34 publications

Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems

Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems

hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

Space‐time stochastic Galerkin boundary elements for acoustic scattering problems

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