Parallel — Vector Variable Bandwidth Equation Solver on Shared Memory Computers

Abstract

In the previous chapter, parallel and vectorized Choleski algorithms which were based on the skyline (column-by-column) storage scheme for shared memory computers (such as the Cray-2, Cray-YMP, Cray-C90, etc..) had been discussed. The factorized algorithms discussed in Chapter 4 have been based upon the “dot product” operations. For certain types of shared memory computers (such as Cray-YMP, Cray-C90, etc.), “Saxpy” operations (to be explained in more detail, later on in this chapter) are known to be faster than “dot product” operations[5.1]. The skyline storage scheme and its associated parallel and vectorized algorithms has been found to prohibit the traditional “loop unrolling” technique used to optimize vector performance, so a less powerful “vector unrolling” strategy was used. This chapter describes a different algorithm that overcomes the deficiency of skyline storage by using a variable bandwidth storage scheme. The objective of this chapter is to describe this new algorithm for solving matrix equations and to demonstrate its accuracy and speed by solving large-scale structural analysis applications on shared memory (such as Cray) supercomputers.