All Categories (1-14 of 14)

1. A Fast Multigrid Approach for Solving the Helmholtz Equation with a Point Source

   04 Feb 2016 | | 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...

2. A Massively Parallel Semicoarsening Multigrid for 3D Reservoir Simulation on Multi-core and Multi-GPU Architectures

   04 Feb 2016 | | 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...

3. 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...

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. 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 and...

6. 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...

7. Illinois Tools: Multigrid Tutorial

   17 Mar 2009 | | Contributor(s):: Nahil Sobh

   Solves the 2D Poisson problem using the Multigrid Method

8. Multigrid Tutorial

   02 Jun 2010 | | Contributor(s):: Dragica Vasileska

   This set of slides describe the idea behind the multigrid method and its implementation.

9. On the Design of a Finite Element Multigrid Solver for Mimetic Finite Difference Schemes

   02 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...

10. Optimal Order Multigrid Preconditioners for Linear Systems Arising in the Semismooth Newton Method Solution Process of a Class of Control-Constrained Problems

    15 Aug 2015 | | 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 control-constrained, quadratic distributed optimal control problems. Using a piecewise constant discretization of the control space, each semismooth...

11. Parallel Multigrid Preconditioner Based on Automatic 3D Tetradedric Meshes

    02 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...

12. Preconditioning for Divergence-Conforming Discretizations of the Stokes Equations

    05 Feb 2016 | | 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 inf-sup stable pairs of finite elements for which weak enforcement of the incompressibility condition implies strong enforcement as well, such as with BDMelements....

13. Quantifying Uncertainties from the Grid in CFD Solutions

    21 Nov 2011 | | Contributor(s):: Tom I-P. Shih

    This talk begins with a study on grid-quality measures that assume grid-induced errors in a CFD solution at a cell is a function of the cell size and shape, the grid distribution around that cell, and the solution computed in the neighborhood of that cell.

14. Understanding the Propagation of Silent Data Corruption in Algebraic Multigrid

    02 Feb 2016 | | 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...