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An incomplete nested dissection algorithm for parallel direct solution of finite element discretizations of partial differential equations (1993)

Mehrabi, M. Reza ; Brown, Robert A.

Springer

Journal of scientific computing 8 (1993), S. 373-387

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ISSN: 1573-7691

Keywords: Domain decomposition ; nested dissection ; LU-factorization ; parallel computers ; MIMD

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Abstract A multilevel algorithm is presented for direct, parallel factorization of the large sparse matrices that arise from finite element and spectral element discretization of elliptic partial differential equations. Incomplete nested dissection and domain decomposition are used to distribute the domain among the processors and to organize the matrix into sections in which pivoting is applied to stabilize the factorization of indefinite equation sets. The algorithm is highly parallel and memory efficient; the efficient use of sparsity in the matrix allows the solution of larger problems as the number of processors is increased, and minimizes computations as well as the number and volume of communications among the processors. The number of messages and the total volume of messages passed during factorization, which are used as measures of algorithm efficiency, are reduced significantly compared to other algorithms. Factorization times are low and speedups high for implementation on an Intel iPSC/860 hypercube computer. Furthermore, the timings for forward and back substitutions are more than an order-of-magnitude smaller than the matrix decomposition times.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01061145

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Statistical microdynamics of extended systems in natural function spaces (1993)

Brown, Robert G. ; Ciftan, Mikael

New York, NY : Wiley-Blackwell

International Journal of Quantum Chemistry 48 (1993), S. 363-375

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ISSN: 0020-7608

Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Notes: An approximate numerical method of solving the Generalized Master Equation for a many-body problem is presented, with examples of its application. This method involves the construction from the full Hamiltonian (of the system plus the “bath”) of a set of unitary Langevin equations that combine deterministic microcanonical, stochastic canonical (heat bath), and stochastic nonthermal dynamics in a single time-integration scheme. If implemented in a representation that captures the essential physics and repeatedly run from a given initial condition, this method evaluates stochastic representatives from the actual fiber bundle of system worldlines that flow from the initial condition and, hence, numerically evaluates the path integral. © 1993 John Wiley & Sons, Inc.

Additional Material: 5 Ill.