"Speedup of computation when solving the nonhomogeneous diffusion equation by a renormalization method"

"Speedup of computation when solving the nonhomogeneous diffusion equation by a renormalization method"
Makarov S.S., Isaeva A.V., Grachev E.A., Serdobolskaya M.L.

A new approximate method of solving an initial-boundary value problem for the nonhomogeneous diffusion equation is proposed. This method is useful in the case when the solution should be found in a region smaller than the support of the source function. The procedure of renormalization of sources in regions far from the region of interest is considered. It is shown how this procedure can decrease the computational costs when solving the initial-boundary value problem. The efficiency of the proposed method is estimated. The dependence of errors of this method on its parameters is analyzed in the case of a two-dimensional region.

Keywords: diffusion equation, numerical methods, renormalization

Makarov S.S. e-mail: sergejsmakarov@gmail.com; Isaeva A.V. e-mail: avisaeva@gmail.com; Grachev E.A. e-mail: grachevea@gmail.com; Serdobolskaya M.L. e-mail serdobolskaya@physics.msu.ru