Performance issues for frontal schemes on a cache-based high performance computer

We consider the implementation of a frontal code for the solution of large sparse unsymmetric linear systems on a high-performance computer where data must be in the cache before arithmetic operations can be performed on it. In particular, we show how we can modify the frontal solution algorithm to enhance the proportion of arithmetic operations performed using Level 3 BLAS thus enabling better reuse of data in the cache. We illustrate the e¤ects of this on Silicon Graphics Power Challenge machines using problems which arise in real engineering and industrial applications. ( 1998 John Wiley & Sons, Ltd. KEY WORDS: unsymmetric sparse matrices; frontal solver; direct methods; Þnite elements; BLAS; computational kernel