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Preconditioning for Divergence-Conforming Discretizations of the Stokes Equations
07 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....
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 , which is capable of handling highly heterogeneous and anisotropic 3D reservoirs, on a parallel architecture with multiple GPU’s. For comparison purposes, the...
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,...
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...
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...
Understanding the Propagation of Silent Data Corruption in Algebraic Multigrid
04 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...
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 | | 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...
Quantifying Uncertainties from the Grid in CFD Solutions
03 Jan 2012 | | 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.
08 Jun 2010 | | Contributor(s):: Dragica Vasileska
This set of slides describe the idea behind the multigrid method and its implementation.
Illinois Tools: Multigrid Tutorial
17 Mar 2009 | | Contributor(s):: Nahil Sobh
Solves the 2D Poisson problem using the Multigrid Method