Abstract
We consider the problem of recovering surface vibrations from acoustic pressure measurements taken in the interior or the exterior of a region. We give two formulations of the problem. One is based on a representation of the pressure as layer potentials and the other is based on approximation by a class of specific solutions to the Helmholtz equation. Boundary element methods are developed to approximate the integral operators. A conjugate gradient algorithm based on Lanczos bidiagonalization is applied to compute regularized solutions to the ill-conditioned equations in the presence of measurement errors. Numerical examples which compare the two formulations are presented.
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