
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...

On the Preconditioning of a HighOrder RDGbased AllSpeed NavierStokes Solver
04 Feb 2016   Contributor(s):: Brian Weston
We investigate the preconditioning of an allspeed NavierStokes solver, based on the orthogonalbasis Reconstructed Discontinuous Galerkin (RDG) space discretization, and integrated using a highorder fullyimplicit time discretization method. The work is motivated by applications in Additive...

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...

Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid
04 Feb 2016   Contributor(s):: Grey Ballard
We consider the sequence of sparse matrixmatrix 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 communicationefficient one for all of the matrix multiplications involved. By...

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...

Spacetime constrained FOSLS with AMGe upscaling
04 Feb 2016   Contributor(s):: Panayot Vassilevski
We consider timedependent PDEs discretized in combined spacetime 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 spacetime). The popular FOSLS (first order system leastsquares)...

Stable Discretizations and Robust Block Preconditioners for FluidStructure Interaction Systems
04 Feb 2016   Contributor(s):: Kai Yang
In our work we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary LagrangianEulerian discretization of some fluidstructure interaction models. After the time discretization, we formulate the fluidstructure interaction equations as saddle point...

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...