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On the Preconditioning of a High-Order RDG-based All-Speed Navier-Stokes Solver
04 Feb 2016 | Online Presentations | 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...
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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...
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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 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...
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Space-time constrained FOSLS with AMGe upscaling
04 Feb 2016 | Online Presentations | 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)...
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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 state-of-the-art subsurface simulation the...
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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 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...
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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 high-dimensional. In this talk, we investigate the improved performance of MLMC versus...
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Stable Discretizations and Robust Block Preconditioners for Fluid-Structure 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 Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point...
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Data-Centric 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...
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New FOSLS Formulation of Nonlinear Stokes Flow for Glaciers
07 Feb 2016 | Online Presentations | Contributor(s): Jeffrey Allen
This talk describes two First-order System Least-squares (FOSLS) formulations of the nonlinear Stokes flow used to model glaciers and ice sheets. The first is a Stress formulation and the second a Stress-Vorticity formulation. Both use fluidity, which is the reciprocal of viscosity and avoid the...
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Non-Blocking 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...
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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 of the incompressibility condition implies strong enforcement as well, such as with BDMelements....
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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...