Parallelization of linear algebra algorithms using ParSol library of mathematical objects

Abstract

The linear algebra problems are an important part of many algorithms, such as numerical solution of PDE systems. In fact, up to 80% or even more of computing time in this kind of algorithms is spent for linear algebra tasks. The paral-lelization of such solvers is the key for parallelization of many advanced algorithms. The mathematical objects library ParSol not only implements some important linear algebra objects in c++, but also allows for semiautomatic parallelization of data parallel and linear algebra algorithms, similar to High Performance Fortran (HPF). ParSol library is applied to implement the finite difference scheme used to solve numerically a system of PDEs describing a nonlinear interaction of two counter-propagating laser waves. Results of computational experiments are presented.