Reconstruction of the scattered field in an inhomogeneous medium
Date Issued
2005
Date
2005
Author(s)
Huang, Yu-Ru
DOI
en-US
Abstract
In problems dealing with the scattering of acoustic waves, we encounter functions known as scattered fields and far fields . In this article, I will derive the scattered field from a given far field pattern where the total field is
governed by the equation Lu+k^2 u=0 outside a domain D. Here, L is an elliptic operator which coincides with the Laplace operator outside a ball of radius R centered at the origin. The derivation of the scattered field is divided into two parts. First, according to known theory in the scattering of acoustic waves, we can derive the scattered field in the region outside of the ball. Then
with the Cauchy data of the scattered field on the boundary of the ball, we will solve the Cauchy problem for the scattered field in the region inside the ball omitting D, and hence we get the complete scattered field.
Subjects
散射波
scattering field
far field
acoustic wave scattering problem
Cauchy problem
Type
thesis
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