Application of the finite element method in a quantitative imaging technique

Article type: Research Article

Authors: Beilina, L.

Affiliations: Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University, SE-42196 Gothenburg, Sweden. E-mail: [email protected]

Abstract: We present the Finite Element Method (FEM) for the numerical solution of the multidimensional coefficient inverse problem (MCIP) in two dimensions. This method is used for explicit reconstruction of the coefficient in the hyperbolic equation using data resulted from a single measurement. To solve our MCIP we use approximate globally convergent method and then apply FEM for the resulted equation. Our numerical examples show quantitative reconstruction of the sound speed in small tumor-like inclusions.

Keywords: Coefficient inverse problem, hyperbolic equation, approximate globally convergent method, finite element method

DOI: 10.3233/JCM-160689

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 16, no. 4, pp. 755-771, 2016