
NonBlocking Conjugate Gradient Methods for Extreme Scale Computing
07 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23536

Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid
07 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23538

Range Decomposition: A Low Communication Algorithm for Solving PDEs on Massively Parallel Machines
07 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23540

A Massively Parallel Semicoarsening Multigrid for 3D Reservoir Simulation on Multicore and MultiGPU Architectures
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23474

On the Design of a Finite Element Multigrid Solver for Mimetic Finite Difference Schemes
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23476

LeastSquares Finite Element Method and Nested Iteration for Electromagnetic TwoFluid Plasma Models
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23478

A Multigrid Method for the SelfAdjoint Angular Flux Form of the RadiationTransport Equation Based on Cellwise Block Jacobi Iteration
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23481

Understanding the Propagation of Silent Data Corruption in Algebraic Multigrid
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23483

A Performance Comparison of Algebraic Multigrid Preconditioners on GPUs and MIC
04 Feb 2016  Online Presentations  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,...
http://nanohub.org/resources/23485

Monolithic Multigrid Methods for Coupled MultiPhysics Problems
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23487

Application of Multigrid Techniques to Magnetic and Electromagnetic Systems
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23489

Geometric Multigrid for MHD Simulations with Nedelec Finite Elements on Tetrahedral Grids
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23491

Parallel Multigrid Preconditioner Based on Automatic 3D Tetradedric Meshes
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23493

HPGMG: Benchmarking Computers Using Multigrid
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23495

A Scalable Algorithm for Inverse Medium Problems with Multiple Sources
04 Feb 2016  Online Presentations  Contributor(s): Keith Kelly
We consider the problem of acoustic scattering as described by the freespace, timeharmonic scalar wave equation given...
http://nanohub.org/resources/23498

Support Graph Smoothing Techniques
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23500

TaskGraph and Functional Programming Models: The New Paradigm
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23502

A Fast Multigrid Approach for Solving the Helmholtz Equation with a Point Source
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23504

Compatible Relaxation Based GeometricAlgebraic Multigrid
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23506

Hub Snub: Removing Vertices with High Degree from Coarsegrid Correction
04 Feb 2016  Online Presentations  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...
http://nanohub.org/resources/23508