A Multithreaded Recursive and Nonrecursive Parallel Sparse Direct Solver

Abstract

Sparse linear system of equations often arises after discretization of the partial differential equations (PDEs) such as computational fluid dynamics, material science, and structural engineering. There are, however, sparse linear systems that are not governed by PDEs, some examples of such applications are circuit simulations, power network analysis, and social network analysis. For solution of sparse linear systems one can choose using either a direct or an iterative method. Direct solvers are based on some factorization of the coefficient matrix such as the LU, QR, or singular value decompositions and are known to be robust. Classical preconditioned iterative solvers, on the other hand, are not as robust as direct solvers and finding an effective preconditioner is often problem dependent. Due to their sequential nature, direct solvers often have limited parallel scalability. In this chapter, we present a new parallel recursive sparse direct solver that is based on the sparse DS factorization. We implement our algorithm using MIT’s Cilk programming language which is also a part of the Intel C++ compiler. We show the scalability and robustness of our algorithm and compare it to Pardiso direct solver.