The SSOR preconditioned conjugate-gradient method on parallel computers

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:6473075

Vaughan, C T

In this dissertation we consider the efficient implementation of iterative methods for solving linear systems of equations on two types of parallel computers: message passing systems, exemplified by the Intel iPSC/1 Hypercube, and local/global memory bus connected systems, exemplified by the Flex/32. The iterative methods being studied are conjugate gradient and m-step SSOR preconditioned conjugate gradient. The class of problems that we are studying are large sparse linear systems of equations arising out of structural analysis problems. We discuss partitioning of the problems to the processors, and present algorithms for efficient implementation of the matrix-vector multiply and the forward and back solves in SSOR for a general symmetric matrix. One way to implement the SSOR preconditioning step is through the use of a multicolor ordering of the unknowns. We will present an algorithm that we have developed to do the multicoloring. To speedup the preconditioned conjugate gradient method for one-step preconditioning, we used three methods for reducing the amount of work per iteration and compared them. We have also extended these methods to m steps of the preconditioner and have analyzed them and compared their performance.

• Research Organization: Virginia Univ., Charlottesville, VA (USA)
• OSTI ID: 6473075
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
990300 -- Information Handling
ALGORITHMS
CHEMICAL ANALYSIS
COMPUTER ARCHITECTURE
COMPUTERS
EQUATIONS
FUNCTIONS
HYPERCUBE COMPUTERS
INFORMATION SYSTEMS
ITERATIVE METHODS
LINEAR PROGRAMMING
MATHEMATICAL LOGIC
MATRIX ELEMENTS
MULTI-ELEMENT ANALYSIS
PARALLEL PROCESSING
PARTITION FUNCTIONS
PROGRAMMING
VECTOR PROCESSING