Geodesic
Organization of parallel computations when solving the inverse problem of wave diagnostics
Numerical methods and programming, Tome 9 (2008) no. 3, pp. 338-345

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This paper deals with the development of methods and algorithms for solving the nonlinear three-dimensional inverse problem of wave diagnostics of irregularities in homogeneous media. A number of approaches used to choose the algorithms and organization of parallel computations for this problem are analyzed. Several numerical algorithms are compared, a method for the formation of the dense matrix of the problem is described, and some procedures employed to tabulate the values of matrix elements on a finite-distance grid and to store intermediate data are discussed. The implemented approaches speed up the algorithms, allow the problem to be solved with 45000 unknowns using up to 500 computing nodes, and makes it possible to perform the model computations for a more complex class of problems. In particular, it becomes possible to model nonlinear effects of wave rereflection.
Keywords: parallel computing, computer simulation, nonlinear wave models, inverse problems, diagnostics, Helmholtz equation. 
@article{VMP_2008_9_3_a13,
     author = {S. L. Ovchinnikov and S. Y. Romanov},
     title = {Organization of parallel computations when solving the inverse problem of wave diagnostics},
     journal = {Numerical methods and programming},
     pages = {338--345},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2008_9_3_a13/}
}
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S. L. Ovchinnikov; S. Y. Romanov. Organization of parallel computations when solving the inverse problem of wave diagnostics. Numerical methods and programming, Tome 9 (2008) no. 3, pp. 338-345. http://geodesic.mathdoc.fr/item/VMP_2008_9_3_a13/