Many scientific programming applications are based on computational models involving nonlinear partial differential equations. These equations are solved via discretization approaches such as the finite element method. The resulting equations lead to nonlinear algebraic systems, which in turn are dealt with by iterative methods. This leads to solving linear algebraic systems involving large-scale sparse matrices. While methods for solving these systems have been studied for decades, there are contemporary practical issues of how to achieve high performance on today’s and future computer architectures. The combination of these areas is an important area of research at the interface of computational and computer science. This paper addresses an important area in computational modeling--semiconductor device simulation--and the application of approaches directed at increasing locality issues in sparse matrices, with the goal of improving overall computational performance.

The paper’s introductory section provides background on both the need for increasing locality and semiconductor simulation software. In the first area, locality optimization packages of Saad--SPARSEKIT2 (for sequential calculations) and PSPARSLIB (for parallel calculations)--are described and used. Comparison with the METIS library for graph partitioning and reordering is also discussed. In terms of the semiconductor area, the paper focuses on the BIPS3D simulator.

The paper proceeds in an orderly manner, discussing related work (for example, the classical Cuthill-McKee algorithm) and issues of caching and optimization. The BIPS3D simulator is presented along with standard profiles of finite element method (FEM) matrices in transistor design. Much of the focus of the paper involves the underlying kernel calculation of the sparse matrix vector product and the relationship to data locality. The authors provide performance results and detailed figures of execution time improvement versus window locality size. The results for various reorderings and iterative techniques (CG, BICGSTAB, and FGMRES) are clearly presented, along with conclusions.

This is an interesting, well-done study on the role of data locality and its use in numerical software, with applications to semiconductor simulation.