A Method For Obtaining A Sparse Matrix
From The Volume Integral Equation For Elastic
Wave Propagation
Author(s)
T. Touhei
Abstract
The advantage of the volume integral equation is that it is possible to clarify
the relationship between fluctuations of the wave field and radiation of scattered
waves. This paper proposes a method to obtain a sparse matrix for the volume
integral equation for elastic wave propagation. The formulation employed here is
based on the wavenumber domain solution together with usage of Haar scaling
functions. The unitarity of the Fourier transform in terms of the Haar scaling
function reveals that the integral equation is transformed into a linear algebraic
equation with a sparse matrix. Numerical calculations are carried out to verify the
proposed formulation.
Keywords: elastic waves, volume integral equation, sparse matrix, unitary
transform, Haar scaling function.
1 Introduction
Since 1980s, the boundary element technique has been recognized as an efficient
tool for the analysis of wave propagation (for example, Brebbia and Walker [3]).
On the other hand, the volume integral equation methods have not been used very
often except for some cases (for example, Kitahara et al [5]). The advantage of
the volume integral equation such as the Lippmann–Schwinger equation (Colton
and Kress [4]) is in that it clarifies the relationship between the fluctuation of the
medium and the radiation of scattered waves. Standard technique for discretizing
the equation, however, leads to a large and dense matrix for the volume integral
equation, that makes sometimes numerical analysis impossible even by recent high
performance computers.
Keywords
elastic waves, volume integral equation, sparse matrix, unitary
transform, Haar scaling function.
Related Book
Other papers in this volume
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