Parallel multigrid method for elliptic difference equations. Anisotropic diffusion

Parallel multigrid method for elliptic difference equations. Anisotropic diffusion We present the development of the parallel multigrid algorithm [1] for solving three-dimensional elliptic difference equations. This algorithm exhibits scalability in the calculation of isotropic problems on multiprocessor supercomputers. Here we improve efficiency of the algorithm for solving anisotropic problems which are typical in applications for modeling the processes of diffusion, heat conduction, fluid dynamics, etc. The developed algorithm is a parallel implementation of the classical multigrid of R.P. Fedorenko for boundary-value problems of the first, second and third kinds, including semi-definite Neumann problem. The algorithm is based on the explicit Chebyshev iterations for solving the coarsest grid equations and to construct smoothing procedures. We develop the adaptive smoothers for anisotropy problems, and show that the multigrid provides efficiency and scalability in parallel implementation.