Poisson equation in a plane polygonal domain is used for modeling many important problems in physics as e.g. electrostatic and magnetostatic field distribution. In this respect, fast and robust solvers for numerical solution of this equation are requested in real world applications. In our paper we propose and analyze such a method. Starting from an initial multigrid-type algorithm first proposed by D. Braess (1981), we construct a full-multigrid method in which we start with an exact solution on a very coarse discretization level of the problem and then interpolate and smooth it on finer ones such that on the finest one we get an approximation of the same order as the discretization scheme used. This is obtained in a number of arithmetic operations of the same order as the dimension of the finest grid matrix, which makes our algorithm much faster than other classical solvers. Numerical experiments are given for a magnetostatic field problem.
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