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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...
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...
Is the Ideal Approximation Operator Always "Ideal" for a Particular C/F Splitting?
04 Feb 2016 | | 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...
Least-Squares Finite Element Method and Nested Iteration for Electromagnetic Two-Fluid Plasma Models
04 Feb 2016 | | Contributor(s):: Christopher Leibs
Efforts are currently being directed towards a fully implicit, electromagnetic, JFNK-based solver, motivating the necessity of developing a fluid-based, electromagnetic, preconditioning strategy . The two-fluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP...
Monolithic Multigrid Methods for Coupled Multi-Physics Problems
04 Feb 2016 | | Contributor(s):: Scott Maclachlan
While block-diagonal and approximate block-factorization preconditioners are often considered for coupled problems, monolithic approaches can offer improved performance, particularly when the coupling between equations is strong. In this talk, we discuss the extension of Braess-Sarazin...
Multilevel Markov Chain Monte Carlo for Uncertainty Quantification in Subsurface Flow
04 Feb 2016 | | 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...
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...
On the Preconditioning of a High-Order RDG-based All-Speed Navier-Stokes Solver
04 Feb 2016 | | 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...
Parallel Multigrid Preconditioner Based on Automatic 3D Tetradedric Meshes
04 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...
Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid
04 Feb 2016 | | 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...
Seventeenth Copper Mountain Conference on Multigrid Methods
04 Feb 2016 |
HIGHLIGHTED TOPICSUncertainty QuantificationOptimization and Inverse ProblemsData Mining, Large Graphs, and Markov ChainsNonsymmetric and Indefinite ProblemsKrylov AcceleratorsHybrid Direct-Iterative Linear SolversParallel Multigrid on Multicore Systems and Heterogeneous ArchitecturesTime...
Space-time constrained FOSLS with AMGe upscaling
04 Feb 2016 | | 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)...
Stable Discretizations and Robust Block Preconditioners for Fluid-Structure Interaction Systems
04 Feb 2016 | | 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...
Support Graph Smoothing Techniques
04 Feb 2016 | | Contributor(s):: Alyson Fox
Many tasks in large-scale network analysis and simulation require efficient approximation of the solution to the linear system $ Lx=b$, where $ L$ is a graph Laplacian. However, due to the large size and complexity of scale-free graphs, standard iterative methods do not perform optimally. The...
Task-Graph and Functional Programming Models: The New Paradigm
04 Feb 2016 | | 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...
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...
[Illinois] CNST Nanotechnology Workshop 2015
04 Feb 2016 | | 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] Nanotechnology meets Biology in the Cancer Cell: Applications in Medicine, Drug Delivery, and Determining Drug Efficacy
04 Feb 2016 | | Contributor(s):: Mostafa El-Sayed
[Illinois] Rare Events with Large-Impact: Bioengineering & Clinical Applications of Circulating Tumor Cells
04 Feb 2016 | | Contributor(s):: Mehmet Toner
[Illinois] Signal Processing at Light Speed: Ultrashort Optical Pulse Generation with Arbitrary Waveforms
29 Jan 2016 | | Contributor(s):: Claire Mcghee
We aim to further improve early detection of cancer biomarkers, including metal ion and small molecules, using functional DNA as the selective component for photonic crystal surface enhanced Raman scattering (PC-SERS) based detection. It is known that gold nanoparticles (AuNPs) display SERS...