Preconditioned multiwavelet Galerkin boundary element solution of Laplace's equation

Amini, S; Nixon, SP

Abstract

In this paper, we study the boundary element solution of Laplace's equation using a Galerkin method with multiwavelet basis functions. This leads to significant matrix compression, requiring computation of only θ(n log n). We also develop a block diagonal preconditioner for the discrete single layer potential which reduces the condition number of the matrix from θ(n) to θ(log2n). We provide numerical results supporting our theory.

Citation

Amini, S., & Nixon, S. (2006). Preconditioned multiwavelet Galerkin boundary element solution of Laplace's equation. Engineering Analysis with Boundary Elements, 30(7), 523-530. https://doi.org/10.1016/j.enganabound.2006.02.003

• Journal Article Type: Article
• Publication Date: Jul 1, 2006
• Deposit Date: Aug 22, 2007
• Journal: Engineering Analysis with Boundary Elements
• Print ISSN: 0955-7997
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 30
• Issue: 7
• Pages: 523-530
• DOI: https://doi.org/10.1016/j.enganabound.2006.02.003
• Keywords: Multiwavelets, matrix compression, boundary element equations, laplace's equation
• Publisher URL: http://dx.doi.org/10.1016/j.enganabound.2006.02.003