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Matthew G. Knepley

  1. Accessible, Extensible, Scalable Tools for Wave Propagation Problems.

    Wed, 11/30/2011 - 15:01 — SomNambul
    Authors: Matthew G. Knepley, David I. Ketcheson, Kyle T. Mandli, Aron Ahmadia, Amal Alghamdi, Manuel Quezada, Matteo Parsani, Matthew Emmett
    Subjects: Numerical Analysis
    Abstract

    Development of scientific software involves tradeoffs between ease of use,
    generality, and performance. We describe the design of a general hyperbolic PDE
    solver that can be operated with the convenience of MATLAB yet achieves
    efficiency near that of hand-coded Fortran and scales to the largest
    supercomputers. This is achieved by using Python for most of the code while
    employing automatically-wrapped Fortran kernels for computationally intensive
    routines, and using Python bindings to interface with a parallel computing
    library and other numerical packages.

  2. Unstructured Geometric Multigrid in Two and Three Dimensions on Complex and Graded Meshes.

    Tue, 04/05/2011 - 15:01 — SomNambul
    Authors: Matthew G. Knepley, Peter R. Brune, L. Ridgway Scott
    Subjects: Numerical Analysis
    Abstract

    The use of multigrid and related preconditioners with the finite element
    method is often limited by the difficulty of applying the algorithm effectively
    to a problem, especially when the domain has a complex shape or adaptive
    refinement. We introduce a simplification of a general topologically-motivated
    mesh coarsening algorithm for use in creating hierarchies of meshes for
    geometric unstructured multigrid methods. The connections between the
    guarantees of this technique and the quality criteria necessary for multigrid
    methods for non-quasi-uniform problems are noted.

  3. Removing the Barrier to Scalability in Parallel FMM.

    Tue, 08/17/2010 - 15:02 — SomNambul
    Authors: Matthew G. Knepley
    Subjects: and Science, Computational Engineering, Finance
    Abstract

    The Fast Multipole Method (FMM) is well known to possess a bottleneck arising
    from decreasing workload on higher levels of the FMM tree [Greengard and Gropp,
    Comp. Math. Appl., 20(7), 1990]. We show that this potential bottleneck can be
    eliminated by overlapping multipole and local expansion computations with
    direct kernel evaluations on the finest level grid.

  4. Biomolecular Electrostatics Simulation by an FMM-based BEM on 512 GPUs.

    Wed, 07/28/2010 - 15:01 — SomNambul
    Authors: Matthew G. Knepley, Rio Yokota, L. A. Barba, Tsuyoshi Hamada, Jaydeep P. Bardhan
    Subjects: and Science, Computational Engineering, Finance
    Abstract

    We present simulations of biomolecular electrostatics at a scale not reached
    before, thanks to both algorithmic and hardware acceleration. The algorithmic
    acceleration is achieved with the fast multipole method (FMM) in conjunction
    with a boundary element method (BEM) formulation of the continuum electrostatic
    model.

  5. PetRBF--A parallel O(N) algorithm for radial basis function interpolation.

    Thu, 10/01/2009 - 00:35 — SomNambul
    Authors: Matthew G. Knepley, Rio Yokota, L. A. Barba
    Subjects: Mathematical Software
    Abstract

    We have developed a parallel algorithm for radial basis function (RBF)
    interpolation that exhibits O(N) complexity,requires O(N) storage, and scales
    excellently up to a thousand processes. The algorithm uses a GMRES iterative
    solver with a restricted additive Schwarz method (RASM) as a preconditioner and
    a fast matrix-vector algorithm. Previous fast RBF methods, --,achieving at most
    O(NlogN) complexity,--, were developed using multiquadric and polyharmonic
    basis functions.

  6. Mesh Algorithms for PDE with Sieve I: Mesh Distribution.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Matthew G. Knepley, Dmitry A. Karpeev
    Subjects: and Science, Computational Engineering, Finance
    Abstract

    We have developed a new programming framework, called Sieve, to support
    parallel numerical PDE algorithms operating over distributed meshes. We have
    also developed a reference implementation of Sieve in C++ as a library of
    generic algorithms operating on distributed containers conforming to the Sieve
    interface. Sieve makes instances of the incidence relation, or \emph{arrows},
    the conceptual first-class objects represented in the containers.

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