Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation

Messner, Matthias; Schanz, Martin; Darve, Eric

doi:10.1016/j.jcp.2011.09.027

Cited by 60 publications

(101 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main conceptual advantage over kernel-dependent decompositions is that the only required knowledge about the kernel is a procedure allowing its evaluation at chosen points. This approach is more recent, and hence less-developed, than the kernel-dependent approach, but oscillatory kernels of type (5) are considered in [30,59], paving the way to application of this "black-box" approach to elastodynamic FMMs.…”

mentioning

confidence: 99%

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

Chaillat

Bonnet

2013

Wave Motion

View full text Add to dashboard Cite

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.

show abstract

mentioning

confidence: 99%

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

Chaillat

Bonnet

2013

Wave Motion

View full text Add to dashboard Cite

show abstract

“…Indeed, as will be shown below, it is generally not a good idea to use the present scheme to represent such kernels in the high-frequency regime. The method can, however, be used in conjunction with the directional FMM scheme in [36], where approximations for kernels of the form g(x)e ık|x| (g smooth) are proposed.…”

Section: Resultsmentioning

confidence: 99%

“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php to obtain an approximation with error bounded by ε in the · ∞ norm. Additionally, (26), (27), and (36) can be used to choose the parameters in such a way that the above conditions are satisfied. This can be done by following the steps in Algorithm 1 below.…”

Section: Error Bound For the Full Approximation Equationmentioning

confidence: 99%

Cauchy Fast Multipole Method for General Analytic Kernels

Létourneau¹,

Cecka²,

Darve³

2014

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

The fast multipole method (FMM) is a technique allowing the fast calculation of long-range interactions between N points in O(N ) or O(N log N ) steps with some prescribed error tolerance. The FMM has found many applications in the field of integral equations and boundary element methods, in particular by accelerating the solution of dense linear systems arising from such formulations. Standard FMMs are derived from analytical expansions of the kernel, for example using spherical harmonics or Taylor expansions. In recent years, the range of applicability and the ease of use of FMMs have been extended by the introduction of black-box and kernel independent techniques. In these approaches, the user provides only a subroutine to numerically calculate the interaction kernel. This allows changing the definition of the kernel with minimal changes to the computer program. This paper presents a novel kernel independent FMM, which leads to diagonal multipoleto-local operators. The result is a significant reduction in the computational cost, particularly when high accuracy is needed. The approach is based on Cauchy's integral formula and the Laplace transform. We will present a numerical analysis of the convergence and numerical results in the case of a multilevel one-dimensional FMM.

show abstract

“…Examples for Laplace, Gauss, and Stokes kernels and radial basis functions, etc., have been presented. It has also been extended to the oscillatory kernels in [12].…”

mentioning

confidence: 99%

“…The presented FMM formulation has two approximations: (1) the interpolation of the kernel functions which is determined by the interpolation order and (2) the low-rank approximation of the M2L operators which is determined by the target accuracy ε. Studies in [12,11] have shown that the setting ( , ε) = (Acc, 10 −Acc ) results approximately in a relative pointwise L 2 error of ε L2 = 10 −Acc . In the rest of the paper we use this convention to describe the accuracy Acc.…”

mentioning

confidence: 99%

Task-Based FMM for Multicore Architectures

Agullo¹,

Bramas²,

Coulaud³

et al. 2014

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

International audienceFast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and hardware. In this paper, we propose a new approach that achieves high performance across architectures. Our method consists of expressing the FMM algorithm as a task flow and employing a state- of-the-art runtime system, StarPU, to process the tasks on the different computing units. We carefully design the task flow, the mathematical operators, their implementations as well as scheduling schemes. Potentials and forces on 200 million particles are computed in 42.3 seconds on a homogeneous 160 cores SGI Altix UV 100 and good scalability is shown

show abstract

Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation

Cited by 60 publications

References 18 publications

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

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

Cauchy Fast Multipole Method for General Analytic Kernels

Task-Based FMM for Multicore Architectures

Contact Info

Product

Resources

About