
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...

A Massively Parallel Semicoarsening Multigrid for 3D Reservoir Simulation on Multicore and MultiGPU 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 [1], which is capable of handling highly heterogeneous and anisotropic 3D reservoirs, on a parallel architecture with multiple GPU’s. For comparison purposes, the...

A Microfluidics Approach to Probing Neuronal Filopodia
12 Apr 2016 

A Multigrid Method for the SelfAdjoint Angular Flux Form of the RadiationTransport Equation Based on Cellwise Block Jacobi Iteration
04 Feb 2016   Contributor(s):: Jeffrey Densmore
Cellwise block Jacobi iteration is a technique for radiationtransport calculations in which the angular flux for all directions is solved for simultaneously within a spatial cell with the angular flux in neighboring cells held fixed. Each step of the iteration then involves the inversion of a...

A Performance Comparison of Algebraic Multigrid Preconditioners on GPUs and MIC
04 Feb 2016   Contributor(s):: Karl Rupp
Algebraic multigrid (AMG) preconditioners for accelerators such as graphics processing units (GPUs) and Intel's manyintegrated core (MIC) architecture typically require a careful, problemdependent tradeoff between efficient hardware use, robustness, and convergence rate in order to...

A Scalable Algorithm for Inverse Medium Problems with Multiple Sources
04 Feb 2016   Contributor(s):: Keith Kelly
We consider the problem of acoustic scattering as described by the freespace, timeharmonic scalar wave equation given by (0.1) along with radiation boundary conditions. Here, is a point in , is the source term, and is the wavenumber. Our formulation is based on potential theory....

Application of Multigrid Techniques to Magnetic and Electromagnetic Systems
04 Feb 2016   Contributor(s):: Benjamin Cowan
We discuss the use of multigrid techniques for several novel systems related to electromagnetics. One of these is the magnetostatic problem, in which systems can involve highly anisotropic and nonlinear materials. We describe the linear problems arising in several variations of this problem,...

BioNanotechnology and Nanomedicine Lecture 25: Force Traction Microscopy
16 Nov 2011   Contributor(s):: Javid Mohammed Ali
BioNanotechnology and Nanomedicine: Applications in Cancer and Mechanobiology provides an introduction to basic concepts of nanotechnology in mechanobiology and in cancer. This is a highly interdisciplinary field of research where knowledge from various disciplines is presented and integrated....

Compatible Relaxation Based GeometricAlgebraic Multigrid
04 Feb 2016   Contributor(s):: Fei Cao
We develop compatible relaxation algorithms for smoothed aggregationbased 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...

DataCentric Models for Multilevel Algorithms
07 Feb 2016   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...

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 ddimensional cube. Using Galerkin discretization, we obtain a linear equation system with unknowns. The corresponding discretization error is in the norm. A major difficulty in...

Geometric Multigrid for MHD Simulations with Nedelec Finite Elements on Tetrahedral Grids
04 Feb 2016   Contributor(s):: Chris Hansen
The MagnetoHydroDynamic (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,...

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 highdimensional. In this talk, we investigate the improved performance of MLMC versus...

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 Coarsegrid 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 illconditioned nature of the systems, obtaining solutions with standard iterative methods is often prohibitively costly; current research aims to automatically construct...

Illinois 2011 NanoBiophotonics Summer School Lecture 1: Welcome
04 Dec 2011   Contributor(s):: Rashid Bashir, Nahil Sobh
1) Prof. Art Kramer, Director  Beckman Institute2) Prof. Ilesanmi Adesida, Dean of Engineering3) Prof. Rashid Bashir, Director  Micro and Nanotechnology Laboratory4) Dr. Marina...

Illinois 2011 NanoBiophotonics Summer School Lecture 2: Photoaucistic Tomography, Ultrasonically Breaking Through the Optical Diffusion Limit
04 Dec 2011   Contributor(s):: Lihong Wang

Illinois 2011 NanoBiophotonics Summer School Lecture 3: Introduction to Cellular Bioengineering
04 Dec 2011   Contributor(s):: Yingxiao Wang

Illinois 2011 NanoBiophotonics Summer School Lecture 4: Pathology of Blood and Tissue Biopsies
04 Dec 2011   Contributor(s):: Krishna Tangella

Illinois 2011 NanoBiophotonics Summer School Lecture 5: Introduction to NanoPhotonics
04 Dec 2011   Contributor(s):: Kent D Choquette