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Preconditioning for Divergence-Conforming 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 inf-sup stable pairs of finite elements for which weak enforcement...
A Massively Parallel Semicoarsening Multigrid for 3D Reservoir Simulation on Multi-core and Multi-GPU 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 , which is capable of handling highly heterogeneous and anisotropic...
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...
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...
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...
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...
Optimal Order Multigrid Preconditioners for Linear Systems Arising in the Semismooth Newton Method Solution Process of a Class of Control-Constrained 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 control-constrained, quadratic distributed optimal...
Quantifying Uncertainties from the Grid in CFD Solutions
03 Jan 2012 | Online Presentations | 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,...
08 Jun 2010 | Teaching Materials | Contributor(s): Dragica Vasileska
This set of slides describe the idea behind the multigrid method and its implementation.
Illinois Tools: Multigrid Tutorial
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19 Mar 2009 | Tools | Contributor(s): Nahil Sobh
Solves the 2D Poisson problem using the Multigrid Method