High performance computation with ADI on cartesian grid to solve the steady state 2D convection diffusion equation

Abstract

We present an ADI type method with structured grids to solve the steady state 2D convection diffusion equation on curved boundary domains. The main objective of this publication, is the design of a highly parallelized method for multi-core implementation. In this paper, we will prescribe the exact solution of the problem in the barycenter of the ghost cells. The massive multi-threading code, takes advantage of the ADI formulation that solve independently 1D problem corresponding to each line or each column. Our aim is to obtain efficient data structures and to create optimal algorithms to avoid the memory bounded problem, providing excellent speed-ups, even for a very large number of cores.