Parallel multigrid method for elliptic difference equations. Part I. Main elements of the algorithm

Multigrid method is widely used for computations of diffusion, fluid dynamics, etc. The parallel implementation of this method may be difficult, especially under conditions of rapid productivity growth and increasing complexity of supercomputer architectures. In order to achieve high performance the scalability requirement arises for running the computer code on parallel computers. Proposed algorithm represents an efficient parallel implementation of the multigrid method of R.P. Fedorenko and is intended for solving three-dimensional elliptic equations. It is considered the boundary value problems including semi-definite Neumann problem. Scalability to a large number of processors is provided by both computational intensity and the logical simplicity of the algorithm. It is achieved by using the explicit Chebyshev iterations as solver of the coarsest grid equations and to construct smoothing procedures. The calculation results are given; they confirm the efficiency of the algorithm and scalability of the parallel code.