Wave Propagation Analysis with Boundary Element Method

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Ledizioni, 2010 - Mathematics - 132 pages
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Time-dependent problems, that are frequently modelled by hyperbolic partial differential equations, can be dealt with the boundary integral equations (BIEs) method.The ideal situation is when the partial differential equation is homogeneous with constant coefficients, the initial conditions vanish and the data are given only on the boundary of a domain independent of time. In this situation the transformation of the differential problem to a BIE follows the same well-known method for elliptic boundary value problems. In fact the starting point for a BIE method is the representation. of the differential problem solution in terms of single layer and double layer potentials using the fundamental solution of the hyperbolic partial differentialoperator.
  

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Contents

Basic theory
1
The onedimensional wave problem
15
The two dimensional wave problem
41
Discretization
75
A Appendix
103
References
116
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