A Template for Scalable Continuum Dynamic Simulations in Multiple GPUs

Abstract

In this work we present a programming philosophy and a template code for achieving computational scalability when using multiple graphics processing units (GPUs) in the numerical solution of any mathematical system of equations found in continuum dynamic simulations. The programming philosophy exploits the principal characteristics of the GPU hardware, with emphasis in the delivering of threads with massive memory fetches, intense calculations using local registers and limited writes to global memory. The philosophy requires explicit formulas for calculations for which domain decomposition is trivial. The domains are decomposed in regions that use the local central processing unit (CPU) to communicate common interfaces using the message passing interface (MPI). A template code for the heat equation is established and tested for scalability. The novelty is that we show a series of codes, constructed from the basic template, that solve all the basic model equations found in continuum dynamics, and present illustrative results. The model equations are the heat equation, the Poisson equation, the shallow-water equations, the flow in porous media equations and the vorticity equations.