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A Fast Multigrid Approach for Solving the Helmholtz Equation with a Point Source
04 Feb 2016 | | 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...
Compatible Relaxation Based Geometric-Algebraic Multigrid
04 Feb 2016 | | 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...
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...
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...
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...
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...
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)...
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...
Discretization of Elliptic Differential Equations Using Sparse Grids and Prewavelets
04 Feb 2016 | | 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...
High Dimensional Uncertainty Quantification via Multilevel Monte Carlo
04 Feb 2016 | | 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...
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...
[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...
[Illinois] Using Photonic Crystals to Enhance SERS Signals for Early Detection of Prostate Cancer
29 Jan 2016 | | Contributor(s):: Caitlin Race
Prostate cancer is the second most common cancer for men, and the second leading cause of death due to cancer in men. Currently, the most common screening method aims to detect high levels of prostate-specific antigen (PSA) in blood. Our research has shown the potential for both better prostate...
[Illinois] Manipulating Substrate Topography for Enhanced Myogenic Differentiation of Primary Myoblasts and Neuromuscular Junction Formation
29 Jan 2016 | | Contributor(s):: Eunkyung Ko
Myogenic commitment of stem cells and primary myoblasts has drawn attention for developing treatments for skeletal muscle diseases. Biophysical cues as well as biochemical cues are known to influence the cellular mechanism of the myogenic differentiation event. Recent studies have revealed that...
[Illinois] Cadherin-Modulated Neural Differentiation of Stem Cells for Neuromuscular Junction Engineering
29 Jan 2016 | | Contributor(s):: Ellen Qin
Recently, efforts are increasingly made to engineer NMJ in vitro for both fundamental and applied bioscience studies. Certain success was made to modulate neural differentiation of stem cells using soluble factors and cell adhesion matrix properties. However, these studies were often plagued by...
[Illinois] Role for Stiffness in Vascular Fate
29 Jan 2016 | | Contributor(s):: Lian Wong
Stem cells, including embryonic stem cells (ESC) and induced pluripotent stem cells, have been explored as tools for studying development, as well as, potential sources for a large number of therapies in regenerative medicine. Traditionally, ESC are cultured on TC-plastic, however; it has been...
[Illinois] Synthetic Optical Holography
26 Jan 2016 | | Contributor(s):: Brad Deutsch
[Illinois] Dimeric Trigger Responsive Drug Conjugate for High Loading Nanoencapsulates
26 Jan 2016 | | Contributor(s):: kaimin Cai
Polymeric micelle is one of the most widely used drug delivery nanomedicine platforms; however, micelle drug delivery systems usually have very low drug loading and poorly defined composition, which greatly limited its further clinical translation. In the course of developing trigger responsive...