Tuning the rank-n update in a wavefront solver for peak performance

The wavefront solver is a type of linear equation solver that is suitable for solving the system of linear equations that arises in many finite-element applications. A new version of the wavefront solver was recently introduced into the ANSYS® program that uses a rank-n update. The rank-n update has properties that allow it to make very efficient use of a hierarchical memory structure. In addition, the rank-n update can exploit both vector and parallel processing to increase its performance. We discuss several general techniques for tuning the rank-n update, using the IBM ES/3090 VF as an example of a computer that incorporates hierarchical memory and vector and parallel processing capabilities. We then report the performance of the tuned rank-n update, both in isolation and in the context of ANSYS jobs.