Numerical analysis of an inverse problem for the eikonal equation

Styles, Vanessa, Elliott, Charles and Deckelnick, Klaus (2011) Numerical analysis of an inverse problem for the eikonal equation. Numerische Mathematik, 119 (2). pp. 245-269. ISSN 0029-599X

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Abstract

We are concerned with the inverse problem for an eikonal equation of determining the speed function using observations of the arrival time on a fixed surface. This is formulated as an optimisation problem for a quadratic functional with the state equation being the eikonal equation coupled to the so-called Soner boundary
condition. The state equation is discretised by a suitable finite difference scheme for which we obtain existence, uniqueness and an error bound. We set up an approximate
optimisation problem and show that a subsequence of the discrete mimina converges to a solution of the continuous optimisation problem as the mesh size goes to zero. The
derivative of the discrete functional is calculated with the help of an adjoint equation which can be solved efficiently by using fast marching techniques. Finally we describe
some numerical results.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Vanessa Styles
Date Deposited: 05 Nov 2012 15:51
Last Modified: 05 Nov 2012 15:51
URI: http://sro.sussex.ac.uk/id/eprint/22717
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