A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation

Journal Article · Sat Feb 28 23:00:00 EST 1987 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0908020· OSTI ID:6560647

Keyes, D E; Gropp, W D

Several preconditioned conjugate gradient (PCG)-based domain decomposition techniques for self-adjoint elliptic partial differential equations in two dimensions are compared against each other and against conventional PCG iterative techniques in serial and parallel contexts. The authors consider preconditioners that make use of fast Poisson solvers on the subdomain interiors. Several preconditioners for the interfacial equations are tested on a set of model problems involving two or four subdomains, which are prototypes of the stripwise and boxwise decompositions of a two-dimensional region. Selected methods have been implemented on the Intel Hypercube by assigning one processor to each subdomain, making use of up to 64 processors. The choice of a ''best'' method for a given problem depends in general upon: (a) the domain geometry, (b) the variability of the operator, and (c) machine characteristics such as the number of processors available and their interconnection scheme, the memory available per processor, and communication and computation rates. Illustrations from the first two categories are provided herein.

• Research Organization: Research Center for Scientific Computation, and Dept. of Mechanical Engineering, Yale Univ., Box 2157, Yale Station, New Haven, CT
• OSTI ID: 6560647
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 8:2; ISSN SIJCD
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
ARRAY PROCESSORS
COMMUNICATIONS
COMPARATIVE EVALUATIONS
COMPUTER ARCHITECTURE
DATA PROCESSING
DATA TRANSMISSION
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUIPMENT INTERFACES
GEOMETRY
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATHEMATICS
MEMORY DEVICES
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
PROCESSING
PROGRAMMING
TWO-DIMENSIONAL CALCULATIONS