Abstract:
Numerical methods for solving volume integral equations describing the problems of wave scattering by transparent obstacles are considered. The equations are approximated using the collocation method on a nonuniform grid, and the problem is reduced to solving a system of linear algebraic equations. An efficient method is proposed for the approximate multiplication of the matrix of this system by a vector, which is comparable in complexity to the method used in the case of a uniform grid. An auxiliary uniform grid is introduced, and methods of interpolation of functions and algorithms of the fast discrete Fourier transform are used. It is essential that the number of nodes of the auxiliary uniform grid is comparable to the number of nodes of the original nonuniform grid.
Key words:volume integral equations, collocation method, nonuniform grid, methods for interpolation of functions, efficient algorithms.
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