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  • 1
    Electronic Resource
    Electronic Resource
    An incomplete nested dissection algorithm for parallel direct solution of finite element discretizations of partial differential equations (1993)
    Springer
    Journal of scientific computing 8 (1993), S. 373-387 
    Details
    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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  • 2
    Electronic Resource
    Electronic Resource
    Parallel implementation of finite-element/newton method for solution of steady-state and transient nonlinear partial differential equations (1995)
    Springer
    Journal of scientific computing 10 (1995), S. 93-137 
    Details
    ISSN: 1573-7691
    Keywords: Domain decomposition ; nested dissection ; LU-factorization ; time integration ; Newton's method ; spectral elements ; finite elements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Domain decomposition by nested dissection for concurrent factorization and storage (CFS) of asymmetric matrices is coupled with finite element and spectral element discretizations and with Newton's method to yield an algorithm for parallel solution of nonlinear initial-and boundary-value problem. The efficiency of the CFS algorithm implemented on a MIMD computer is demonstrated by analysis of the solution of the two-dimensional, Poisson equation discretized using both finite and spectral elements. Computation rates and speedups for the LU-decomposition algorithm, which is the most time consuming portion of the solution algorithm, scale with the number of processors. The spectral element discretization with high-order interpolating polynomials yields especially high speedups because the ratio of communication to computation is lower than for low-order finite element discretizations. The robustness of the parallel implementation of the finite-element/Newton algorithm is demonstrated by solution of steady and transient natural convection in a two-dimensional cavity, a standard test problem for low Prandtl number convection. Time integration is performed using a fully implicit algorithm with a modified Newton's method for solution of nonlinear equations at each time step. The efficiency of the CFS version of the finite-element/Newton algorithm compares well with a spectral element algorithm implemented on a MIMD computer using iterative matrix methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02087962
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  • 3
    Electronic Resource
    Electronic Resource
    Statistical microdynamics of extended systems in natural function spaces (1993)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 48 (1993), S. 363-375 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560480837
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  • 4
    Electronic Resource
    Electronic Resource
    A generalized non-muffin-tin theory of band structureThis work was supported by the U.S. Army Research Office. (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 87-104 
    Details
    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: A generalized non-muffin-tin band structure method is presented in the context of multiple scattering off of the Wigner-Seitz cell. This technique has the following desirable features: it is formally exact and rapidly convergent; it preserves the separation between the nondiagonal scattering matrix for the cell and the usual structure constants of KKR in the secular determinant; it produces an accurate representation of the wave function throughout the sphere bounding the Wigner-Seitz cell and hence is suitable for self-consistent field calculations and applications that require a detailed knowledge of the unperturbed crystal potential and wave functions. Various aspects of the application of this theory to the empty lattice and sodium are presented, and its limitations discussed. Some future lines of research are briefly reviewed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560260813
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  • 5
    Electronic Resource
    Electronic Resource
    A generalized non-muffin-tin theory of band structure (1985)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 803-804 
    Details
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560270614
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