Applied Scientific Research — Department of Defense SBIR Phase I: The simulation of nearly all physical processes eventually leads to the evaluation of a li

Description

The simulation of nearly all physical processes eventually leads to the evaluation of a linear system of equations of the form Ax = b, the vast majority of which involve sparse banded matrices. To this end, while highly optimized parallel algorithms are currently available for the solution of very large system of equations in a distributed computing environment, very little has been done to date on algorithms that run efficiently on multi-core CPUs. As such there are new opportunities to develop fast, cache aware, shared memory algorithms for the solution of sparse linear equations on multi-core CPUs. The objective of this Phase I proposal is to investigate the relative performances of multigrid and Krylov based linear solvers using existing technologies, and to propose strategies for follow on development work during Phase II. Additionally, a fast, cache-aware Krylov solver will be developed for multi-core CPUs as demonstration of feasibility for Phase II.