Fast Evaluation of Volume Potentials in Boundary Element Methods

Of, Günther; Steinbach, Olaf; Urthaler, Peter

doi:10.1137/080744359

Cited by 21 publications

(10 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the evaluation of the correlation always involves the evaluation of the potential, a fast algorithm is required here as well. This can also be realized by the use of the fast multipole method, see [20].…”

Section: Resultsmentioning

confidence: 99%

Rapid computation of far-field statistics for random obstacle scattering

Harbrecht

Ilić

Multerer

2019

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

In this article, we consider the numerical approximation of far-field statistics for acoustic scattering problems in the case of random obstacles. In particular, we consider the computation of the expected far-field pattern and the expected scattered wave away from the scatterer as well as the computation of the corresponding variances. To that end, we introduce an artificial interface, which almost surely contains all realizations of the random scatterer. At this interface, we directly approximate the second order statistics, i.e., the expectation and the variance, of the Cauchy data by means of boundary integral equations. From these quantities, we are able to rapidly evaluate statistics of the scattered wave everywhere in the exterior domain, including the expectation and the variance of the far-field. By employing a low-rank approximation of the Cauchy data's twopoint correlation function, we drastically reduce the cost of the computation of the scattered wave's variance. Numerical results are provided in order to demonstrate the feasibility of the proposed approach.

show abstract

Section: Resultsmentioning

confidence: 99%

Rapid computation of far-field statistics for random obstacle scattering

Harbrecht

Ilić

Multerer

2019

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

show abstract

“…in order to approximate N 1 and to avoid volume integrals. We refer the interested reader to [27] for more details. For a pure Dirichlet problem, i.e.…”

Section: Boundary Elementmentioning

confidence: 99%

Vlasov--Poisson System Tackled by Particle Simulation Utilizing Boundary Element Methods

Keßler¹,

Rjasanow²,

Weißer³

2020

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov-Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution function. Whereas the advection of the particles is grid-free by its very nature, the computation of the acceleration involves the solution of the non-local Poisson equation. To circumvent a volume mesh, we utilise the Fast Boundary Element Method, which reduces the three-dimensional Poisson equation to a system of linear equations on its twodimensional boundary. This gives rise to fully populated matrices which are approximated by the H 2 -technique, reducing the computational time from quadratic to linear complexity. The approximation scheme based on interpolation has shown to be robust and flexible, allowing a straightforward generalisation to vector-valued functions. In particular, the Coulomb forces acting on the particles are computed in linear complexity. In first numerical tests, we validate our approach with the help of classical non-linear plasma phenomena. Furthermore, we show that our method is able to simulate electron plasmas in complex three-dimensional domains with mixed boundary conditions in linear complexity.

show abstract

“…Further details can be found in previous papers [39,41]. For the volume term, the Galerkin form can be exploited by interchanging of the order of integration [31]…”

Section: Numerics: Remainder Volume Integralmentioning

confidence: 99%

Boundary integral analysis for non-homogeneous, incompressible Stokes flows

Gray

Jakowski²,

Moore

et al. 2019

Adv Comput Math

View full text Add to dashboard Cite

A regular-grid volume-integration algorithm is developed for the non-homogeneous 3D Stokes equation. Based upon the observation that the Stokeslet U is the Laplacian of a function H, the volume integral is reformulated as a simple boundary integral, plus a remainder domain integral. The modified source term in this remainder integral is everywhere zero on the boundary and can therefore be continuously extended as zero to a regular grid covering the domain. The volume integral can then be evaluated on the grid. Applying this method to the Navier-Stokes equations will require obtaining velocity gradients, and thus an efficient algorithm for post-processing these derivatives is also discussed. To validate the numerical implementation, test results employing a linear element Galerkin approximation are presented.

show abstract

Fast Evaluation of Volume Potentials in Boundary Element Methods

Cited by 21 publications

References 25 publications

Rapid computation of far-field statistics for random obstacle scattering

Rapid computation of far-field statistics for random obstacle scattering

Vlasov--Poisson System Tackled by Particle Simulation Utilizing Boundary Element Methods

Boundary integral analysis for non-homogeneous, incompressible Stokes flows

Contact Info

Product

Resources

About