Implementation and use of high-performance parallel skyline matrix subroutines on the IBM vector facility

Abstract

Skyline matrix storage format is widely used by computer programs which do finite element analysis. The popularity of skyline format stems from its simplicity, compactness, and efficiency. Even with these advantages, skyline matrix factorization and solution often consumes large amounts of processing time in finite element analysis programs. To reduce the sometimes overwhelming processing requirements of finite element analysis programs, high-performance skyline matrix subroutines were developed specifically for the IBM ES/3090™ and ES/9000™ processors. Both symmetric and unsymmetric skyline matrices are supported. These subroutines, which became available in Release 4 of IBM's Engineering and Scientific Subroutine Library (ESSL), achieve high performance through vector and parallel processing. Serial vector performance of these routines is over two times that of conventional methods, and parallel processing amplifies the vector performance with a high degree of efficiency. General strategies for achieving similar levels of performance are presented; these strategies are applicable in certain ways to other algorithms and other computers. Also presented are benchmark results for the symmetric skyline routine alone and in combination with three finite element analysis programs.