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  1. Non-Blocking Conjugate Gradient Methods for Extreme Scale Computing

    07 Feb 2016 | | Contributor(s):: Paul Eller

    Many scientific and engineering applications use Krylov subspace methods to solve large systems of linear equations. For extreme scale parallel computing systems, the dot products in these methods (implemented using allreduce operations in MPI) can limit performance because they are a...

  2. Preconditioning for Divergence-Conforming Discretizations of the Stokes Equations

    07 Feb 2016 | | Contributor(s):: Thomas Benson

    Recent years have seen renewed interest in the numerical solution of the Stokes Equations. Of particular interest is the use of inf-sup stable pairs of finite elements for which weak enforcement of the incompressibility condition implies strong enforcement as well, such as with BDMelements....

  3. Range Decomposition: A Low Communication Algorithm for Solving PDEs on Massively Parallel Machines

    07 Feb 2016 | | Contributor(s):: Tom Manteuffel

    The Range Decomposition (RD) algorithm uses nested iteration and adaptive mesh refinement locally before performing a global communication step. Only several such steps are observed to be necessary before reaching a solution within a small multiple of discretization error. The target application...

  4. A Fast Multigrid Approach for Solving the Helmholtz Equation with a Point Source

    04 Feb 2016 | | Contributor(s):: Eran Treister

    Solving the discretized Helmholtz equations with high wave numbers in large dimensions is a challenging task. However, in many scenarios, the solution of these equations is required for a point source. In this case, the problem can be be reformulated and split into two parts: one in a solution...

  5. A Massively Parallel Semicoarsening Multigrid for 3D Reservoir Simulation on Multi-core and Multi-GPU Architectures

    04 Feb 2016 | | Contributor(s):: Abdulrahman Manea

    In this work, we have designed and implemented a massively parallel version of the Semicoarsening Black Box Multigrid Solver [1], which is capable of handling highly heterogeneous and anisotropic 3D reservoirs, on a parallel architecture with multiple GPU’s. For comparison purposes, the...

  6. A Multigrid Method for the Self-Adjoint Angular Flux Form of the Radiation-Transport Equation Based on Cellwise Block Jacobi Iteration

    04 Feb 2016 | | Contributor(s):: Jeffrey Densmore

    Cellwise block Jacobi iteration is a technique for radiation-transport calculations in which the angular flux for all directions is solved for simultaneously within a spatial cell with the angular flux in neighboring cells held fixed. Each step of the iteration then involves the inversion of a...

  7. A Performance Comparison of Algebraic Multigrid Preconditioners on GPUs and MIC

    04 Feb 2016 | | Contributor(s):: Karl Rupp

    Algebraic multigrid (AMG) preconditioners for accelerators such as graphics processing units (GPUs) and Intel's many-integrated core (MIC) architecture typically require a careful, problem-dependent trade-off between efficient hardware use, robustness, and convergence rate in order to...

  8. A Scalable Algorithm for Inverse Medium Problems with Multiple Sources

    04 Feb 2016 | | Contributor(s):: Keith Kelly

    We consider the problem of acoustic scattering as described by the free-space, time-harmonic scalar wave equation given by   (0.1)   along with radiation boundary conditions. Here, is a point in , is the source term, and is the wavenumber. Our formulation is based on potential theory....

  9. Application of Multigrid Techniques to Magnetic and Electromagnetic Systems

    04 Feb 2016 | | Contributor(s):: Benjamin Cowan

    We discuss the use of multigrid techniques for several novel systems related to electromagnetics. One of these is the magnetostatic problem, in which systems can involve highly anisotropic and nonlinear materials. We describe the linear problems arising in several variations of this problem,...

  10. Compatible Relaxation Based Geometric-Algebraic Multigrid

    04 Feb 2016 | | Contributor(s):: Fei Cao

    We develop compatible relaxation algorithms for smoothed aggregation-based multigrid coarsening. In the proposed method, we use the geometry of the given discrete problem on the finest level to coarsen the system together with compatible relaxation to from the sparsity structure of the...

  11. Discretization of Elliptic Differential Equations Using Sparse Grids and Prewavelets

    04 Feb 2016 | | Contributor(s):: Christoph Pflaum

    Sparse grids can be used to discretize second order elliptic differential equations on a d-dimensional cube. Using Galerkin discretization, we obtain a linear equation system with  unknowns. The corresponding discretization error is  in the -norm. A major difficulty in...

  12. Geometric Multigrid for MHD Simulations with Nedelec Finite Elements on Tetrahedral Grids

    04 Feb 2016 | | Contributor(s):: Chris Hansen

    The Magneto-HydroDynamic (MHD) model is used extensively to simulate macroscopic plasma dynamics in Magnetic Confinement Fusion (MCF) devices. In these simulations, the span of time scales from fast wave dynamics to the desired evolution of equilibrium due to transport processes is large,...

  13. High Dimensional Uncertainty Quantification via Multilevel Monte Carlo

    04 Feb 2016 | | Contributor(s):: Hillary Fairbanks

    Multilevel Monte Carlo (MLMC) has been shown to be a cost effective way to compute moments of desired quantities of interest in stochastic partial differential equations when the uncertainty in the data is high-dimensional. In this talk, we investigate the improved performance of MLMC versus...

  14. HPGMG: Benchmarking Computers Using Multigrid

    04 Feb 2016 | | Contributor(s):: Jed Brown

    HPGMG (https://hpgmg.org) is a geometric multigrid benchmark designed to measure the performance and versatility of computers. For a benchmark to be representative of applications, good performance on the benchmark should be sufficient to ensure good performance on most important applications...

  15. Hub Snub: Removing Vertices with High Degree from Coarse-grid Correction

    04 Feb 2016 | | Contributor(s):: Geoffry Sanders

    Network scientists often employ numerical solutions to linear systems as subroutines of data mining algorithms. Due to the ill-conditioned nature of the systems, obtaining solutions with standard iterative methods is often prohibitively costly; current research aims to automatically construct...

  16. Is the Ideal Approximation Operator Always "Ideal" for a Particular C/F Splitting?

    04 Feb 2016 | | Contributor(s):: Erin Molloy

    Given a coarse grid, the ideal prolongation operator is defined by , where the weight matrix,  , interpolates a set of fine grid variable (-points) from a set of coarse grid variable (-points), and the identity matrix, , represents the injection of -points to and from...

  17. Least-Squares Finite Element Method and Nested Iteration for Electromagnetic Two-Fluid Plasma Models

    04 Feb 2016 | | Contributor(s):: Christopher Leibs

    Efforts are currently being directed towards a fully implicit, electromagnetic, JFNK-based solver, motivating the necessity of developing a fluid-based, electromagnetic, preconditioning strategy [1]. The two-fluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP...

  18. Monolithic Multigrid Methods for Coupled Multi-Physics Problems

    04 Feb 2016 | | Contributor(s):: Scott Maclachlan

    While block-diagonal and approximate block-factorization preconditioners are often considered for coupled problems, monolithic approaches can offer improved performance, particularly when the coupling between equations is strong. In this talk, we discuss the extension of Braess-Sarazin...

  19. Multilevel Markov Chain Monte Carlo for Uncertainty Quantification in Subsurface Flow

    04 Feb 2016 | | Contributor(s):: Christian Ketelsen

    The multilevel Monte Carlo method has been shown to be an effective variance reduction technique for quantifying uncertainty in subsurface flow simulations when the random conductivity field can be represented by a simple prior distribution. In state-of-the-art subsurface simulation the...

  20. On the Design of a Finite Element Multigrid Solver for Mimetic Finite Difference Schemes

    04 Feb 2016 | | Contributor(s):: Carmen Rodrigo

    The focus of this work is to study the relation between mimetic finite difference schemes on triangular grids and some finite element methods for two model problems based on curl-rot and grad-div operators. With this purpose, modified Nédélec and Raviart-Thomas finite element...