A parallel algorithm for solving linear equations arising from one-dimensional network problems

Conference · Tue Jan 01 04:00:00 EST 1991

OSTI ID:5860608

Mesina, G L

One-dimensional (1-D) network problems, such as those arising from 1- D fluid simulations and electrical circuitry, produce systems of sparse linear equations which are nearly tridiagonal and contain a few non-zero entries outside the tridiagonal. Most direct solution techniques for such problems either do not take advantage of the special structure of the matrix or do not fully utilize parallel computer architectures. We describe a new parallel direct linear equation solution algorithm, called TRBR, which is especially designed to take advantage of this structure on MIMD shared memory machines. The new method belongs to a family of methods which split the coefficient matrix into the sum of a tridiagonal matrix T and a matrix comprised of the remaining coefficients R. Efficient tridiagonal methods are used to algebraically simplify the linear system. A smaller auxiliary subsystem is created and solved and its solution is used to calculate the solution of the original system. The newly devised BR method solves the subsystem. The serial and parallel operation counts are given for the new method and related earlier methods. TRBR is shown to have the smallest operation count in this class of direct methods. Numerical results are given. Although the algorithm is designed for one-dimensional networks, it has been applied successfully to three-dimensional problems as well. 20 refs., 2 figs., 4 tabs.

• Research Organization: EG and G Idaho, Inc., Idaho Falls, ID (USA)
• Sponsoring Organization: DOE; USDOE, Washington, DC (USA)
• DOE Contract Number: AC07-76ID01570
• OSTI ID: 5860608
• Report Number(s): EGG-M-90383; CONF-910414--36; ON: DE91012815
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
FLUID FLOW
MATHEMATICAL LOGIC
MATRICES
NUCLEAR FACILITIES
NUCLEAR POWER PLANTS
NUMERICAL SOLUTION
PARALLEL PROCESSING
POWER PLANTS
PROGRAMMING
THERMAL POWER PLANTS