Solution of the first-order form of the 3-D discrete ordinates equations on a massively parallel machine

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

OSTI ID:5611956

Koch, K R; Baker, R S; Alcouffe, R E

A common approach used today to solve the neutron transport equation is to apply the discrete ordinates method, with source iteration, to the first-order form of the transport equation. Although the use of synthetic acceleration greatly reduces the number of source iterations required for convergence, we have found that the time spent in inverting the transport operator still forms a large part of the overall computational effort. In today's production codes, this inversion is performed directly through the use of a transport sweep. Although a transport sweep is inherently a sequential operation, sweep algorithms which successfully vectorize (i.e., diagonal line sweeps) have been developed and implemented for vector machines such as the CRAY. However, with the advent of massively parallel SIMD architectures, it has been the accepted belief that an efficient algorithm for direct inversion of the transport operator could not be successfully adapted to machines such as the CM-2. Instead, interest has focused on alternative approaches to solving the transport equation, such as the second-order (even parity) form, or response matrix methods, which require an iterative inversion of the transport operator. The purpose of this paper is to show that an efficient algorithm for the solution of the standard, first-order form of the transport equation does exist for massively parallel architectures, and that the direct inversion of the transport operator can indeed be successfully parallelized.

• Research Organization: Los Alamos National Lab., NM (United States)
• Sponsoring Organization: DOE; USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5611956
• Report Number(s): LA-UR-91-4157; CONF-920606--2; ON: DE92004575
• Country of Publication: United States
• Language: English

Related Subjects

663610* -- Neutron Physics-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
ARRAY PROCESSORS
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
NEUTRON DIFFUSION EQUATION
PARALLEL PROCESSING
PROGRAMMING