
NonBlocking 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...

Preconditioning for DivergenceConforming 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 infsup stable pairs of finite elements for which weak enforcement of the incompressibility condition implies strong enforcement as well, such as with BDMelements....

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...

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...

A Massively Parallel Semicoarsening Multigrid for 3D Reservoir Simulation on Multicore and MultiGPU 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...

A Multigrid Method for the SelfAdjoint Angular Flux Form of the RadiationTransport Equation Based on Cellwise Block Jacobi Iteration
04 Feb 2016   Contributor(s):: Jeffrey Densmore
Cellwise block Jacobi iteration is a technique for radiationtransport 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...

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 manyintegrated core (MIC) architecture typically require a careful, problemdependent tradeoff between efficient hardware use, robustness, and convergence rate in order to...

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 freespace, timeharmonic 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....

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,...

Compatible Relaxation Based GeometricAlgebraic Multigrid
04 Feb 2016   Contributor(s):: Fei Cao
We develop compatible relaxation algorithms for smoothed aggregationbased 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...

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 ddimensional cube. Using Galerkin discretization, we obtain a linear equation system with unknowns. The corresponding discretization error is in the norm. A major difficulty in...

Geometric Multigrid for MHD Simulations with Nedelec Finite Elements on Tetrahedral Grids
04 Feb 2016   Contributor(s):: Chris Hansen
The MagnetoHydroDynamic (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,...

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 highdimensional. In this talk, we investigate the improved performance of MLMC versus...

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...

Hub Snub: Removing Vertices with High Degree from Coarsegrid 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 illconditioned nature of the systems, obtaining solutions with standard iterative methods is often prohibitively costly; current research aims to automatically construct...

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...

LeastSquares Finite Element Method and Nested Iteration for Electromagnetic TwoFluid Plasma Models
04 Feb 2016   Contributor(s):: Christopher Leibs
Efforts are currently being directed towards a fully implicit, electromagnetic, JFNKbased solver, motivating the necessity of developing a fluidbased, electromagnetic, preconditioning strategy [1]. The twofluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP...

Monolithic Multigrid Methods for Coupled MultiPhysics Problems
04 Feb 2016   Contributor(s):: Scott Maclachlan
While blockdiagonal and approximate blockfactorization 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 BraessSarazin...

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 stateoftheart subsurface simulation the...

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 curlrot and graddiv operators. With this purpose, modified Nédélec and RaviartThomas finite element...