Parallel sparse LU factorization in a shared memory computing environment

The time consuming part of a semiconductor process and device simulation usually consists of solving a series of sparse, structurally symmetric linear systems. This paper presents a parallel sparse LU factorization on shared memory parallel multiprocessor machines. The parallel programming model is based on OpenMP, a portable alternative to message passing. High sequential and parallel computational performance are an essential goal. Although the algorithm is designed for sparse matrices, the solver achieves up to 70% of the parallel Linpack performance on a sixteen-processor SGI Origin 2000 for realistic three-dimensional problems. For problems arising from 3D semiconductor device simulations, we demonstrate factorization rates of 0.9, 2.7, 1.0, 2.2 Gigaflop/s, reached on an eight-processor Cray J90, a twenty-processor SGI Origin 2000, a four-processor DEC AlphaServer 8400-5/440, and an eight-processor DEG AlphaServer 8400-5/625, respectively.