On Development of Parallel Algorithms for Solving Parabolic and Elliptic Equations

Abstract

In this paper, we present results of the development of certain parallel numerical methods for solving three-dimensional evolutionary and stationary problems of diffusion and heat transfer. We present a detailed description of a special, explicit iteration scheme for parabolic equations and discuss a multigrid technology used for solving elliptic equations and implicit schemes for parabolic equations.

Coarse grid corrections in Krylov subspace evaluations of the matrix exponential

“…Fedorenko [11,12], the first papers describing the multigrid method as we know it now [21, Section 10.9.2], is devoted to the solution of Poisson equations arising in time integration of 2D incompressible hydrodynamics equations [13]. Currently, multigrid methods form a major tool for efficient implementation of implicit and semi-implicit time integration schemes on parallel supercomputers [2,17,36,35].…”