Geodesic
Boundary elements method based on a preliminary discretization
Matematičeskoe modelirovanie, Tome 25 (2013) no. 9, pp. 17-31

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A new numerical method is presented for solving diffraction problems. The method is based on the boundary elements idea, i.e. the unknown values are the field values on the surface of the scatterer. Instead of numerical approximation of the initial (continuous) problem, an analogue of boundary element method is constructed for an approximate lattice problem. As the result, the accuracy of the method decreases, but it becomes very easy for implementation since the Green's function stop being singular. For uniqueness of the solution, the method is constructed by analogy with the CFIE approach developed for the classical boundary element method.
Mots-clés : wave diffraction
Keywords: Helmholtz equation, boundary elements method, boundary algebraic equations. 
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     author = {J. Poblet-Puig and V. Yu. Valyaev and A. V. Shanin},
     title = {Boundary elements method based on a preliminary discretization},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {17--31},
     publisher = {mathdoc},
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     number = {9},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_9_a2/}
}
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J. Poblet-Puig; V. Yu. Valyaev; A. V. Shanin. Boundary elements method based on a preliminary discretization. Matematičeskoe modelirovanie, Tome 25 (2013) no. 9, pp. 17-31. http://geodesic.mathdoc.fr/item/MM_2013_25_9_a2/