In this master's thesis the multigrid method is presented on a model problem of solving Poisson's equation with finite difference method. With suitable iterative method we obtain numerical approximation of solution, which is corrected with a correction calculated on coarse grid. In addition to the basic principles of the multigrid method some others variations of the method are derived together with its numerical efficiency. The reduction of high frequency component of the error by the local smoothing factor using local Fourier analysis is derived together with asymptotic convergence factor. Numerical examples of solving other variations of Poisson's are presented at the end of the thesis.
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