NUMERICAL SOLUTION OF AN INVERSE INITIAL BOUNDARY VALUE PROBLEM FOR THE WAVE EQUATION IN THE PRESENCE OF CONDUCTIVITY IMPERFECTIONS OF SMALL VOLUME

作者：Asch Mark^*; Darbas Marion; Duval Jean Baptiste

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2011, 17(4): 1016-1034.

DOI：10.1051/cocv/2010031

• Wave equation
• exact controllability
• inverse problem
• finite elements
• Fourier inversion

We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of "limited-view" data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing the centers of the imperfections. Numerical results, in 2- and 3-D, show the robustness and accuracy of the approach for retrieving randomly placed imperfections from both complete and partial boundary measurements.

• 出版日期2011-10