Hybrid FEM/FDM method for an inverse scattering problem

L. Beilina and C. Johnsson
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L. Beilina: Chalmers University of Technology
C. Johnsson: Chalmers University of Technology

A chapter in Numerical Mathematics and Advanced Applications, 2003, pp 545-556 from Springer

Abstract: Summary We apply an adaptive hybrid FEM/FDM method to an inverse scattering problem for the time-dependent acoustic wave equation in 2D and 3D, where we seek to reconstruct an unknown sound velocity c(x) from measured wave-reflection data. Typically,this corresponds to identifying an unknown object (scatterer) in a surrounding homogeneous medium. We use an optimal control approach where we seek a sound velocity c(x) which minimizes the difference between computed and measured output data in a discrete L 2 norm. We solve the optimization problem by a gradient method where in each step we compute the gradient by solving a forward (direct) and a backward (adjoint) wave propagation problem. To compute the backward and forward wave propagation problems we use an adaptive hybrid finite element/finite difference method, where we exploit the flexibility of mesh refinement and adaption of the finite element method in a domain covering the object, and the efficiency of a structured mesh finite difference method in the surrounding homogeneous domain. The hybrid scheme can be viewed as a finite element scheme on a partially unstructured mesh which gives a stable coupling of the two methods. We use an adaptive mesh refinement algorithm to improve the accuracy of the reconstruction and speed up the convergence of the gradient method.

Keywords: Observation Point; Unstructured Mesh; Posteriori Error Estimate; Absorb Boundary Condition; Adjoint Problem (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-2089-4_51

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DOI: 10.1007/978-88-470-2089-4_51

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