Abstract:
The article is devoted to development of a parallel multigrid algorithm for numerical solution of (non)linear initial-boundary value problems (implicit schemes) based on the
Robust Multigrid Technique (RMT). Advantage of the proposed algorithm is opportunity
of parallel solution of boundary value problems and initial-boundary value problems in
unified manner using $m=1,2,3,\dots$ independent computers (threads, if parallelization technology OpenMP used). Coarse grids are generated only in space, the number of grid levels depends on the coefficient matrix condition number of the resulting system of linear
algebraic equations. Point Gauss-Seidel method is used as a smoothing procedure for
solving the initial-boundary value problem for the heat conductivity equation. Description of the algorithm and results of computational experiments performed using the
OpenMP technology are given.
Keywords:initial boundary value problems, parallel computing, multigrid methods.