Tags: UIUC

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  1. 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,...

  2. Compatible Relaxation Based Geometric-Algebraic Multigrid

    04 Feb 2016 | | 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...

  3. 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 d-dimensional cube. Using Galerkin discretization, we obtain a linear equation system with  unknowns. The corresponding discretization error is  in the -norm. A major difficulty in...

  4. Geometric Multigrid for MHD Simulations with Nedelec Finite Elements on Tetrahedral Grids

    04 Feb 2016 | | 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,...

  5. 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 high-dimensional. In this talk, we investigate the improved performance of MLMC versus...

  6. 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...

  7. Hub Snub: Removing Vertices with High Degree from Coarse-grid 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 ill-conditioned nature of the systems, obtaining solutions with standard iterative methods is often prohibitively costly; current research aims to automatically construct...

  8. 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...

  9. Least-Squares Finite Element Method and Nested Iteration for Electromagnetic Two-Fluid Plasma Models

    04 Feb 2016 | | 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 [1]. The two-fluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP...

  10. Monolithic Multigrid Methods for Coupled Multi-Physics Problems

    04 Feb 2016 | | 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...

  11. 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 state-of-the-art subsurface simulation the...

  12. 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 curl-rot and grad-div operators. With this purpose, modified Nédélec and Raviart-Thomas finite element...

  13. On the Preconditioning of a High-Order RDG-based All-Speed Navier-Stokes Solver

    04 Feb 2016 | | 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...

  14. 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...

  15. Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid

    04 Feb 2016 | | 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...

  16. 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 Direct-Iterative Linear SolversParallel Multigrid on Multicore Systems and Heterogeneous ArchitecturesTime...

  17. Space-time constrained FOSLS with AMGe upscaling

    04 Feb 2016 | | 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)...

  18. Stable Discretizations and Robust Block Preconditioners for Fluid-Structure 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 Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point...

  19. Support Graph Smoothing Techniques

    04 Feb 2016 | | 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...

  20. Task-Graph and Functional Programming Models: The New Paradigm

    04 Feb 2016 | | 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...