Multi-level Boundary Element Methods
Author(s)
G. F. Dargush & M. M. Grigoriev
Abstract
A new class of fast boundary element methods has been developed by the
authors as an extension of the Brandt and Lubrecht multi-level multi-integration
algorithm to mixed boundary value problems in irregular domains. Here,
emphasis is placed on the presentation of three numerical examples, involving
the potential Stokes and Helmholtz kernels. These model problems are intended
to illuminate both the benefits and limitations of the resulting multi-level
boundary element methods.
1 Introduction
Standard boundary element techniques require two major steps to obtain a
numerical solution, namely, forming a global boundary element matrix by
integrating kernels over the boundary elements, and solving the matrix set itself.
Let N represent the total number of boundary degrees of freedom in a typical
problem. Then the former step is normally of order 2 ( ) O N operations, while the
latter one requires 3 ( ) O N operations when using direct procedures based upon
Gauss elimination. For relatively small N , traditional boundary element
methods are fast and practical even on a single-processor workstation or a
personal computer. However, due to the complexity of the standard algorithms,
one finds that the performance of conventional boundary element formulations
deteriorates quickly with problem size. Solutions for 5 10 N > become difficult,
even on state-of-the-art supercomputers. On the other hand, many problems of
practical importance require fine boundary element meshes leading to very large
numbers of degrees of freedom.
Keywords
Related Book
Other papers in this volume
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