Wavelet compression of parabolic diffusion integral kernels

Abstract

In this paper we examine the properties of steady and unsteady diffusion fundamental solutions in the framework of fast BEM. The fundamental solutions and their kernels form integral kernels in boundary integral equations. The properties of these kernels define the relationship between CPU time and storage gain versus the accuracy of sparse approximations in fast BEM. We show that, when solving a diffusion type problem, using unsteady fundamental solutions is advantageous over steady fundamental solutions. We examine the behaviour of fundamental solutions to show why the unsteady fundamental solution is better for fast BEM. Furthermore, we confirm the theoretical findings by simulation of viscous fluid flow and heat transfer. We consider steady cases, where a false transient approach is used so unsteady diffusion fundamental solutions may be employed. Finally, we examine cases of increasing non-linearity, to highlight that these findings apply to strongly nonlinear problems as well.