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....
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...
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...
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...
05 Feb 2016 | Tools | Contributor(s): Scott Michael Louis Slone, Chris Maffeo, AbderRahman N Sobh, Aleksei Aksimentiev
Tool workflow for building DNA Brick structures automatically.
[Illinois] CNST Nanotechnology Workshop 2015
04 Feb 2016 | Workshops | Contributor(s): Mustafa El-sayed, Mehmet Toner
The CNST Nanotechnology Workshop highlights University of Illinois research in bionanotechnology and nanomedicine, nanoelectronics and nanophotonics, and nanomaterials and nanomanufacturing, leading to cross-campus and industry collaborations.
[Illinois] Rare Events with Large-Impact: Bioengineering & Clinical Applications of Circulating Tumor Cells
04 Feb 2016 | Online Presentations | Contributor(s): Mehmet Toner
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...
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...
Plasmonics and Metasurfaces for Extreme Manipulation of Light
08 Mar 2016 | Online Presentations | Contributor(s): Yongmin Liu
In this talk, I will present some of our work in the fascinating field of plasmonics and optical metasurfaces. First, I will discuss reconfigurable plasmonic lenses operating in microfluidic environment, which can dynamically diverge, collimate and focus surface plasmons . Second, I will...
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...
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...
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)...
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...
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...
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...
Hub Snub: Removing Vertices with High Degree from Coarse-grid Correction
04 Feb 2016 | Online Presentations | 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...
Compatible Relaxation Based Geometric-Algebraic Multigrid
04 Feb 2016 | Online Presentations | 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...
A Fast Multigrid Approach for Solving the Helmholtz Equation with a Point Source
04 Feb 2016 | Online Presentations | 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...
Task-Graph and Functional Programming Models: The New Paradigm
04 Feb 2016 | Online Presentations | 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...