Space-time constrained FOSLS with AMGe upscaling
04 Feb 2016 | Online Presentations | Contributor(s): Panayot Vassilevski
We consider time-dependent PDEs discretized in combined space-time domains. We first reduce the PDE to a first order system. Very often in practice, one of the equations of the reduced system involves the divergence operator (in space-time). The popular FOSLS (first order system least-squares)...
Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid
04 Feb 2016 | Online Presentations | Contributor(s): Grey Ballard
We consider the sequence of sparse matrix-matrix multiplications performed during the setup phase of algebraic multigrid. In particular, we show that the most commonly used parallel algorithm is often not the most communication-efficient one for all of the matrix multiplications involved. By...
Is the Ideal Approximation Operator Always "Ideal" for a Particular C/F Splitting?
04 Feb 2016 | Online Presentations | 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...
On the Preconditioning of a High-Order RDG-based All-Speed Navier-Stokes Solver
04 Feb 2016 | Online Presentations | Contributor(s): Brian Weston
We investigate the preconditioning of an all-speed Navier-Stokes solver, based on the orthogonal-basis Reconstructed Discontinuous Galerkin (RDG) space discretization, and integrated using a high-order fully-implicit time discretization method. The work is motivated by applications in Additive...
Hub Snub: Removing Vertices with High Degree from Coarse-grid 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 ill-conditioned nature of the systems, obtaining solutions with standard iterative methods is often prohibitively costly; current research aims to automatically construct...
Compatible Relaxation Based Geometric-Algebraic Multigrid
04 Feb 2016 | Online Presentations | 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...
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 source. In this case, the problem can be be reformulated and split into two parts: one in a solution...
Task-Graph 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 distributed-memory communication model that has served us well through the CISC processor era. However, because of MPI's low-level interface, which requires the user to manage raw memory buffers, and its bulk-synchronous communication...
Support Graph Smoothing Techniques
04 Feb 2016 | Online Presentations | Contributor(s): Alyson Fox
Many tasks in large-scale 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 scale-free graphs, standard iterative methods do not perform optimally. The...
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 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....
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 performance on the benchmark should be sufficient to ensure good performance on most important applications...
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 with the efficiency of GMG lead us to the development of an Hybrid Multigrid preconditionner. From...
Geometric Multigrid for MHD Simulations with Nedelec Finite Elements on Tetrahedral Grids
04 Feb 2016 | Online Presentations | 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,...
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 nonlinear materials. We describe the linear problems arising in several variations of this problem,...
Monolithic Multigrid Methods for Coupled Multi-Physics Problems
04 Feb 2016 | Online Presentations | 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...
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 many-integrated core (MIC) architecture typically require a careful, problem-dependent trade-off between efficient hardware use, robustness, and convergence rate in order to...
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 heterogeneous processing elements that operate at near-threshold-voltage to meet power constraints. The...
A Multigrid Method for the Self-Adjoint Angular Flux Form of the Radiation-Transport Equation Based on Cellwise Block Jacobi Iteration
04 Feb 2016 | Online Presentations | 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...
Least-Squares Finite Element Method and Nested Iteration for Electromagnetic Two-Fluid Plasma Models
04 Feb 2016 | Online Presentations | 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 . The two-fluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP...
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 curl-rot and grad-div operators. With this purpose, modified Nédélec and Raviart-Thomas finite element...