Geodesic
The inverse problem of acoustic diagnosis for three-dimensional media
Numerical methods and programming, Tome 7 (2006) no. 1, pp. 113-121.

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Methods and algorithms for solving the direct and inverse problems of acoustic diagnosis for three-dimensional media on parallel computers are discussed. The inverse problem is considered in nonlinear formulation for the Helmholtz equation with unknown coefficient. Highly efficient and linearly scalable algorithms were developed for solving the direct and inverse problems under discussion. This allows one to significantly reduce computing cost, to enhance the problem dimension by several orders, and to optimize the parameters of model experiments. The work was supported by the Russian Foundation for Basic Research (05-01-08068).
Keywords: computer simulation, wave models, inverse problems of acoustic diagnosis, parallel computing, Helmholtz equation, dense block matrices. 
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A. V. Goncharsky; S. Y. Romanov; S. A. Kharchenko. The inverse problem of acoustic diagnosis for three-dimensional media. Numerical methods and programming, Tome 7 (2006) no. 1, pp. 113-121. http://geodesic.mathdoc.fr/item/VMP_2006_7_1_a13/