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A moving pseudo-boundary method of fundamental solutions for void detection. (English) Zbl 1268.65161
Summary: We propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a void. This problem can be modeled as an inverse boundary value problem for harmonic functions. The algorithm for imaging the interior of the medium also makes use of radial polar parametrization of the unknown void shape in two dimensions. The center of this radial polar parametrization is considered to be unknown. We also include the contraction and dilation factors to be part of the unknowns in the resulting nonlinear least-squares problem. This approach addresses the major problem of locating the pseudo-boundary in the MFS in a natural way, because the inverse problem in question is nonlinear anyway. The feasibility of this new method is illustrated by several numerical examples.

MSC:
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
Software:
HYBRJ; Matlab; minpack
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