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Center for Nonlinear Studies |
Modern computer simulation methods require increasingly greater speed and accuracy and are being applied to extraordinarily large system of equations, with tens or hundreds of millions of unknowns. To solve these systems massively parallel computers, and algorithms that effectively exploit their power, are essential. It is recognized that solvers based on the multigrid strategy are very efficient iterative schemes which possess an optimal computational complexity. We developed the multigrid preconditioner for Preconditioned Conjugate Gradient (PCG) method which guarantees the independence of the iteration number on the mesh step size. The algorithm can be naturally parallelized without significant modifications. The numerical experiments show the competitiveness of our algorithm based on the comparison with such popular method as Algebraic Multigrid (AMG).