
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...

Seventeenth Copper Mountain Conference on Multigrid Methods
04 Feb 2016 
HIGHLIGHTED TOPICSUncertainty QuantificationOptimization and Inverse ProblemsData Mining, Large Graphs, and Markov ChainsNonsymmetric and Indefinite ProblemsKrylov AcceleratorsHybrid DirectIterative Linear SolversParallel Multigrid on Multicore Systems and Heterogeneous ArchitecturesTime...

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...

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...

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...

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...

Understanding the Propagation of Silent Data Corruption in Algebraic Multigrid
04 Feb 2016   Contributor(s):: Jon Calhoun
Sparse linear solvers from a fundamental kernel in high performance computing (HPC). Exascale systems are expected to be more complex than systems of today being composed of thousands of heterogeneous processing elements that operate at nearthresholdvoltage to meet power constraints. The...

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...

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...

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,...

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,...

Parallel Multigrid Preconditioner Based on Automatic 3D Tetradedric Meshes
04 Feb 2016   Contributor(s):: Frederic Vi
Multigrid methods are efficient for solving large sparse linear systems. Geometric (GMG) and Algebraic Multigrid (AMG) have both their own benefits and limitations. Combining the simplicity of AMG with the efficiency of GMG lead us to the development of an Hybrid Multigrid preconditionner. From...

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...

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....

Support Graph Smoothing Techniques
04 Feb 2016   Contributor(s):: Alyson Fox
Many tasks in largescale network analysis and simulation require efficient approximation of the solution to the linear system $ Lx=b$, where $ L$ is a graph Laplacian. However, due to the large size and complexity of scalefree graphs, standard iterative methods do not perform optimally. The...

TaskGraph and Functional Programming Models: The New Paradigm
04 Feb 2016   Contributor(s):: Ben Bergen
The Message Passing Interface (MPI) is an example of a distributedmemory communication model that has served us well through the CISC processor era. However, because of MPI's lowlevel interface, which requires the user to manage raw memory buffers, and its bulksynchronous communication...

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...

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...