On fast matrix–vector multiplication in wavelet Galerkin BEM

Xiao, Jinyou; Wen, Liu; Tausch, Johannes

doi:10.1016/j.enganabound.2008.05.006

Cited by 15 publications

(16 citation statements)

References 20 publications

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“…We have shown that, by using the wavelets with QVMs and the a-posteriori compression, the memory requirement of the WGBEM can be reduced by a factor greater than six. The resulting memory requirement is typically less than that of the FMM being transformed from the WGBEM [21]. Moreover, after compressions the complexity of the method scales almost linearly.…”

Section: Resultsmentioning

confidence: 86%

“…Here we compare the memory allocation of both methods. This is based on the fact that the two methods can be transformed from each other [21]. In WGBEM most memory is used to store the NS-form while in the FMM most memory goes into storing direct interactions of neighboring cubes in the finest level.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Further results in this direction can be found in [18][19][20]. The relation between the WGBEM and the method based on lowrank approximation, e.g., FMM, is discussed in [21].…”

Section: Introductionmentioning

confidence: 99%

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A-posteriori compression of wavelet-BEM matrices

Xiao¹,

Tausch²,

Hu³

2009

Comput Mech

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The success of the wavelet boundary element method (BEM) depends on its matrix compression capability. The wavelet Galerkin BEM (WGBEM) based on nonstandard form (NS-form) in Tausch (J Numer Math 12(3): 233-254, 2004) has almost linear memory and time complexity. Recently, wavelets with the quasi-vanishing moments (QVMs) have been used to decrease the constant factors involved in the complexity estimates (Xiao in Comput Methods Appl Mech Eng 197:4000-4006, 2008). However, the representations of layer potentials in QVM bases still have much more negligible entries than predicted by a-priori estimates, which are based on the separation of the supports of the source-and test-wavelets. In this paper, we introduce an a-posteriori compression strategy, which is designed to preserve the convergence properties of the underlying Galerkin discretization scheme. We summarize the different compression schemes for the WGBEM and demonstrate their performances on practical problems including Stokes flow, acoustic scattering and capacitance extraction. Numerical results show that memory allocation and CPU time can be reduced several times. Thus the storage for the NS-form is typically less than what is required to store the near-field interactions in the well-known fast multipole method.

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Section: Resultsmentioning

confidence: 86%

Section: Numerical Examplesmentioning

confidence: 99%

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A-posteriori compression of wavelet-BEM matrices

Xiao¹,

Tausch²,

Hu³

2009

Comput Mech

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“…However, some of the nonzero entries of the sparse matrix still have small values which cannot affect the order of convergence of the wavelet Galerkin BEM. By setting some entries to zero for which the difference of the wavelet levels is sufficiently large, a sparser matrix can be obtained, which contains only O(N) nonzero entries [19,22,28,29].…”

Section: Matrix Compressionmentioning

confidence: 99%

A multiwavelet Galerkin boundary element method for the stationary Stokes problem in 3D

Zhu

2011

Engineering Analysis with Boundary Elements

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“…The relation between the WGBEM and the method based on low-rank approximation, e.g. FMM, is discussed in [32].…”

Section: Introductionmentioning

confidence: 99%

Combined equivalent charge formulations and fast wavelet Galerkin BEM for 3‐D electrostatic analysis

Xiao

Tausch

Cao

et al. 2009

Numerical Meth Engineering

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SUMMARYWe describe a new equivalent charge formulation (ECF), i.e. the combined ECF (CECF), for electrostatic analysis of structures consisting of conductors and dielectrics. The CECF uses a weighted combination of the single-and the adjoint double-layer operators to account for the potential on the conductor-dielectric surface and is found to have better conditioning than the standard ECF. A perturbation approach is presented to insure that the capacitances are computed accurately even when the permittivity ratios of the dielectrics are vary large. Unlike the original perturbation approach, this new approach uses only one system matrix with different right-hand sides.A wavelet Galerkin boundary element method (WGBEM) for solving the ECF and CECF is developed based on the new variable-order WGBEM introduced in (J. Several numerical examples show that the proposed CECF converges faster than the ECF, and that the WGBEM, using both the ECF and CECF, has almost linear complexity in solving large-scale 3-D electrostatic problems. Moreover, since the truncated non-standard form is computed once and then stored, the WGBEM is very suitable for solving problems with multiple right-hand sides, like the perturbation approach in this paper.

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On fast matrix–vector multiplication in wavelet Galerkin BEM

Cited by 15 publications

References 20 publications

A-posteriori compression of wavelet-BEM matrices

A-posteriori compression of wavelet-BEM matrices

A multiwavelet Galerkin boundary element method for the stationary Stokes problem in 3D

Combined equivalent charge formulations and fast wavelet Galerkin BEM for 3‐D electrostatic analysis

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