Multilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects

Tong, Mei Song; Chew, Weng Cho

doi:10.1016/j.jcp.2008.10.003

Cited by 34 publications

(29 citation statements)

References 34 publications

(37 reference statements)

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“…Industry puts a limit to both, inspiring the quest for ever more powerful methods. To overcome the CUP timing and memory requirement the 3D full wave solver Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm (NSPWMLFMA) is used in this work [13][14][15]. By employing NSPWMLFMA, the complexity is reduced from O(N 2 ) to the order of O(N log N ) at all frequencies [15,16].…”

Section: Introductionmentioning

confidence: 99%

“…To overcome the CUP timing and memory requirement the 3D full wave solver Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm (NSPWMLFMA) is used in this work [13][14][15]. By employing NSPWMLFMA, the complexity is reduced from O(N 2 ) to the order of O(N log N ) at all frequencies [15,16]. In addition to this, the entire implementation (both the setup and the solution of the iterative process), has been parallelized using an asynchronous algorithm, such that all simulations can be solved efficiently on a cluster of computers.…”

Section: Introductionmentioning

confidence: 99%

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Simulation and Experimental Verification of W-Band Finite Frequency Selective Surfaces on Infinite Background With 3d Full Wave Solver Nspwmlfma

Islam¹,

Stiens²,

Poesen³

et al. 2010

PIER

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Abstract-We present the design, processing and testing of a W-band finite by infinite and a finite by finite Grounded Frequency Selective Surfaces (FSSs) on infinite background. The 3D full wave solver Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm (NSPWMLFMA) is used to simulate the FSSs. As NSPWMLFMA solver improves the complexity matrix-vector product in an iterative solver from O(N 2 ) to O(N log N ) which enables the solver to simulate finite arrays with faster execution time and manageable memory requirements. The simulation results were verified by comparing them with the experimental results. The comparisons demonstrate the accuracy of the NSPWMLFMA solver.We fabricated the corresponding FSS arrays on quartz substrate with photolithographic etching techniques and characterized the vector S-parameters with a free space Millimeter Wave Vector Network Analyzer (MVNA).

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulation and Experimental Verification of W-Band Finite Frequency Selective Surfaces on Infinite Background With 3d Full Wave Solver Nspwmlfma

Islam¹,

Stiens²,

Poesen³

et al. 2010

PIER

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show abstract

“…Early developments of the diagonal-form decomposition for 3D elastodynamics were presented in [37], with applications to the scattering of seismic waves by basins and topographies. Improved versions of this approach were more recently proposed in [19,82], with numerical examples involving BE models of size up to N = O(10 6 ). Moreover, a 2D elastodynamic version of the wideband approach has been recently proposed in [77], while periodic 3D elastodynamic problems are addressed in [46] using a low-frequency separable decomposition of periodic Green's tensors.…”

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confidence: 99%

Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics

Chaillat

Bonnet

2013

Wave Motion

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To cite this version:Stéphanie Chaillat, Marc Bonnet. Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics. Wave Motion, Elsevier, 2013Elsevier, , 50, pp.1090Elsevier, -1104 Abstract This article is mainly devoted to a review on fast BEMs for elastodynamics, with particular attention on time-harmonic fast multipole methods (FMMs). It also includes original results that complete a very recent study on the FMM for elastodynamic problems in semi-infinite media. The main concepts underlying fast elastodynamic BEMs and the kernel-dependent elastodynamic FM-BEM based on the diagonal-form kernel decomposition are reviewed. An elastodynamic FM-BEM based on the half-space Green's tensor suitable for semi-infinite media, and in particular on the fast evaluation of the corresponding governing double-layer integral operator involved in the BIE formulation of wave scattering by underground cavities, is then presented. Results on numerical tests for the multipole evaluation of the half-space traction Green's tensor and the FMM treatment of a sample 3D problem involving wave scattering by an underground cavity demonstrate the accuracy of the proposed approach. The article concludes with a discussion of several topics open to further investigation, with relevant published work surveyed in the process.

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“…The standard weak formulation of (2.16) reads: Given 17) where the sesquilinear form 18) and the linear functional F (v) on (H 1/2 (Γ)) 2 is defined by…”

Section: Weak Formulationmentioning

confidence: 99%

“…To effectively reduce the BIE into a linear system, many different solvers including the boundary element method (BEM) ( [13]), the Nyströme method ( [16]), the fast multipole method [5,17] and the spectral method ( [12]) have been considered.…”

Section: Introductionmentioning

confidence: 99%

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

Bao

Yin

2017

Journal of Computational Physics

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Multilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects

Cited by 34 publications

References 34 publications

Simulation and Experimental Verification of W-Band Finite Frequency Selective Surfaces on Infinite Background With 3d Full Wave Solver Nspwmlfma

Simulation and Experimental Verification of W-Band Finite Frequency Selective Surfaces on Infinite Background With 3d Full Wave Solver Nspwmlfma

Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

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