
Optimal Order Multigrid Preconditioners for Linear Systems Arising in the Semismooth Newton Method Solution Process of a Class of ControlConstrained Problems
18 Aug 2015  Online Presentations  Contributor(s): Andrei Draganescu
In this work we present a new multigrid preconditioner for the linear systems arising in the semismooth Newton method solution process of certain controlconstrained, quadratic distributed optimal control problems. Using a piecewise constant discretization of the control space, each semismooth...

Multilevel Solvers for High Resolution Electric Field Calculations
18 Aug 2015  Online Presentations  Contributor(s): Andrew Reisner
High fidelity electric field calculations are a critical component in plasma simulations. In this this talk we consider the problem of a dielectric barrier discharge (DBD) wherein the electric field is calculated to support a compressible flow, thus requiring a highly efficient global solve. The...

Iterative Solution Method for an Implicit Orbit Averaged ParticleinCell Model
18 Aug 2015  Online Presentations  Contributor(s): Benjamin Sturdevant
Present kinetic simulations of turbulence in magnetized plasmas employ models from gyrokinetic theory, which is based on a number of ordering assumptions used to reduce the VlasovMaxwell system to eliminate high frequency phenomena. Recently, a second order accurate, implicit particleincell...

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 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  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 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  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 [1]. The twofluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP model...

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 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  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 nearthresholdvoltage to meet power constraints. The...

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, problemdependent tradeoff between efficient hardware use, robustness, and convergence rate in order to...

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 coupling between equations is strong. In this talk, we discuss the extension of BraessSarazin relaxation...

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,...

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 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  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...

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 and...

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 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  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 size and complexity of scalefree graphs, standard iterative methods do not perform optimally. The use...

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 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  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 of...

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 coarsen the system together with compatible relaxation to from the sparsity structure of the...

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 iterative methods is often prohibitively costly; current research aims to automatically construct...

On the Preconditioning of a HighOrder RDGbased AllSpeed NavierStokes Solver
04 Feb 2016  Online Presentations  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...

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 the...

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 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...

Spacetime constrained FOSLS with AMGe upscaling
04 Feb 2016  Online Presentations  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)...

Multilevel Markov Chain Monte Carlo for Uncertainty Quantification in Subsurface Flow
04 Feb 2016  Online Presentations  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...

Discretization of Elliptic Differential Equations Using Sparse Grids and Prewavelets
04 Feb 2016  Online Presentations  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...

High Dimensional Uncertainty Quantification via Multilevel Monte Carlo
04 Feb 2016  Online Presentations  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...

Stable Discretizations and Robust Block Preconditioners for FluidStructure Interaction Systems
04 Feb 2016  Online Presentations  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...

DataCentric Models for Multilevel Algorithms
07 Feb 2016  Online Presentations  Contributor(s): Samuel Guiterrez
Today, computational scientists must contend with a diverse set of supercomputer architectures that are capable of exposing unprecedented levels of parallelism and complexity. Effectively placing, moving, and operating on data residing in complex distributed memory hierarchies is quickly becoming...

New FOSLS Formulation of Nonlinear Stokes Flow for Glaciers
07 Feb 2016  Online Presentations  Contributor(s): Jeffrey Allen
This talk describes two Firstorder System Leastsquares (FOSLS) formulations of the nonlinear Stokes flow used to model glaciers and ice sheets. The first is a Stress formulation and the second a StressVorticity formulation. Both use fluidity, which is the reciprocal of viscosity and avoid the...

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 (implemented using allreduce operations in MPI) can limit performance because they are a...

Preconditioning for DivergenceConforming Discretizations of the Stokes Equations
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 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  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 necessary before reaching a solution within a small multiple of discretization error. The target application...