Generalization of adaptive cross approximation for time‐domain boundary element methods

Abstract

A numerical approach to the solution of the wave equation is performed by means of the boundary element method. In the interest of increasing the efficiency of this method a low‐rank approximation such as the adaptive cross approximation is carried out. We discuss a generalization of the adaptive cross approximation to approximate a three‐dimensional array of data. In particular, we perform an approximation of an array of boundary element matrices in the Laplace domain. The proposed scheme is illustrated by preliminary numerical experiments.

Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation

“…In this article, we present a novel approach which relies on hierarchical low-rank approximation in both space and frequency. The main idea is to reformulate the problem of approximating the convolution weights as a tensor approximation problem [31]. By means of H 2 -matrices in space and ACA in frequency, we manage to reduce the complexity to almost linear in the number of degrees of freedom as well as in the number of time steps.…”

Boundary Element Methods for the Wave Equation based on Hierarchical Matrices and Adaptive Cross Approximation

“…In this article, we present a novel approach which relies on hierarchical low-rank approximation in both space and frequency. The main idea is to reformulate the problem of approximating the convolution weights as a tensor approximation problem [42]. By means of H 2 -matrices in space and ACA in frequency, we manage to reduce the complexity to almost linear in the number of degrees of freedom as well as in the number of time steps.…”