Architecture Aware Parallelization of Solvers for PDE Systems on Geometrical Graphs in Diana Simulation Environment

Abstract

Solving PDEs on geometrical graphs with method of lines approach leads to large-scale, homogeneous, weakly connected ODE systems. Such differential equation systems can be efficiently solved on parallel computers by exploiting of parallelism across system. In this case optimal parallelization of the ODE solvers is equivalent to finding an optimal mapping of secondary topology graph on architecture graph. Architecture aware graph partitioning is a relatively new direction of research. Available solutions do not cover all the most important hardware platforms. Furthermore, usage of existing architecture aware partitioners does not provide facilities for estimating discretization parameters in PDE solvers. In this paper, we discuss an approach to overcome above-mentioned drawbacks.