Parallel scheduling of the PCG method for banded matrices rising from FDM/FEM

An implicit time-linearized finite difference discretization of partial differential equations on regular/structured meshes results in an n-diagonal block system of algebraic equations, which is usually solved by means of the Preconditioned Conjugate Gradient (PCG) method. In this paper, an analysis of the parallel implementation of this method on several computer architectures and for several programming paradigms is presented. For three-dimensional regular/structured meshes, a new implementation of the PCG method with Jacobi preconditioner is proposed. For the computer architectures and number of processors employed in this study, it has been found that this implementation is more efficient than the standard one, and can be applied to narrow-band matrices and other preconditioners, such as, for example, polynomial ones.