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Whether you're simulating the electronic structure of a carbon nanotube or the strain within an automobile part, the
calculations usually boil down to a simple matrix equation,
Ax = f. The faster you can fill the
matrix A with the coefficients for your partial
differential equation (PDE), and the faster you can solve for
the vector x given a forcing function f, the faster you have your overall solution. Things get interesting when the matrix A is too large to fit in the memory available on one machine, or when the coefficients in A cause the matrix to be ill-conditioned.
Ax = f
Many different algorithms have been developed to map a PDE onto a matrix, to pre-condition the matrix to a better form, and to solve the matrix with blinding speed. Different algorithms usually exploit some property of the matrix, such as symmetry, to reduce either memory requirements or solution speed or both.
Learn more about algorithms from the many resources on this site, listed below.
Computational Mathematics: Role, Impact, Challenges
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20 Dec 2007 | Online Presentations | Contributor(s): Juan C. Meza
This presentation was one of 13 presentations in the one-day forum,
"Excellence in Computer Simulation," which brought together a broad
set of experts to reflect on the future of...
Hierarchical Temporal Memory: How a New Theory of Neocortex May Lead to Truly Intelligent Machines
12 Dec 2007 | Online Presentations | Contributor(s): Jeff Hawkins
Coaxing computers to perorm basic acts of perception and robotics, let alone high-level thought, has been difficult. No existing computer can recognize pictures, understand language, or navigate...
HPCW Introduction to Parallel Programming with MPI
05 Dec 2007 | Online Presentations | Contributor(s): David Seaman
illustrating message-passing techniques. The examples include point-to-point
and collective communication using blocking and nonblocking transmission. One
Computing the Horribleness of Soft Condensed Matter
5.0 out of 5 stars
19 Oct 2007 | Online Presentations | Contributor(s): Eric Jakobsson
A great triumph of computer simulations 40 years ago was to make the liquid state of matter understandable in terms of physical
interactions between individual molecules. Prior to the first...
HPCW Parallel Programming Models
09 Oct 2007 | Online Presentations | Contributor(s): Sam Midkiff
Computing Research Institute
Rosen Center for Advanced Computing
MCW07 Simple Models for Molecular Transport Junctions
13 Sep 2007 | Online Presentations | Contributor(s): Misha Galperin, Abraham Nitzan, Mark A. Ratner
We review our recent research on role of interactions in molecular transport junctions. We consider simple models within nonequilibrium Green function approach (NEGF) in steady-state regime.
MCW07 Electronic Level Alignment at Metal-Molecule Contacts with a GW Approach
05 Sep 2007 | Online Presentations | Contributor(s): Jeffrey B. Neaton
Most recent theoretical studies of electron transport in single-molecule junctions rely on a Landauer approach, simplified to treat electron-electron interactions at a mean-field level within...
SUGAR: the SPICE for MEMS
21 May 2007 | Online Presentations | Contributor(s): Jason Clark
In this seminar, I present some design, modeling, and simulation features of a computer aided engineering tool for microelectromechanical systems (MEMS) called SUGAR. For experimental...
Modeling and Analysis of VLSI Interconnects
10 May 2007 | Online Presentations | Contributor(s): Cheng-Kok Koh
With continual technology scaling, the accurate and efficient modeling and simulation of interconnect effects have become problems of central importance. In order to accurately model the...
Renormalization Group Theories of Strongly Interacting Electronic Structure
20 Apr 2007 | Online Presentations | Contributor(s): Garnet Chan, NCN SLC@Northwestern
Our work is in the area of the electronic structure and dynamics of complex processes. We engage in developing new and more powerful theoretical techniques which enable us to describe strong...
Is Seeing Believing? How to Think Visually and Analyze with Both Your Eyes and Brain
26 Mar 2007 | Online Presentations | Contributor(s): David Ebert
This presentation will cover the basic techniques, and some of the available tools, for visualization, and will explain how to avoid miscommunicating information from visualizations.
Surprises on the nanoscale: Plasmonic waves that travel backward and spin birefringence without magnetic fields
29 Jan 2007 | Online Presentations | Contributor(s): Daniel Neuhauser
As nanonphotonics and nanoelectronics are pushed down towards the
molecular scale, interesting effects emerge. We discuss how
birefringence (different propagation of two polarizations) is...
Understanding Phonon Dynamics via 1D Atomic Chains
28 Aug 2006 | Online Presentations | Contributor(s): Timothy S Fisher
Phonons are the principal carriers of thermal energy in semiconductors and insulators, and they serve a vital role in dissipating heat produced by scattered electrons in semiconductor devices....
NEMO 3D: Intel optimizations and Multiple Quantum Dot Simulations
14 Aug 2006 | Online Presentations | Contributor(s): Anish Dhanekula, Gerhard Klimeck
NEMO-3D is a nanoelectronic modeling tool that analyzes the electronic structure of nanoscopic devices. Nanoelectronic devices such as Quantum Dots (QDs) can contain millions of atoms,. Therefore,...
Autonomic Adaptation of Virtual Distributed Environments in a Multi-Domain Infrastructure
11 Jul 2006 | Online Presentations | Contributor(s): Ryan Riley, Dongyan Xu
By federating resources from multiple domains, a shared infrastructure provides aggregated computation resources to a large number of users. With rapid advances in virtualization technologies, we...
Exploring Electron Transfer with Density Functional Theory
03 Jul 2006 | Online Presentations | Contributor(s): Troy Van Voorhis
This talk will highlight several illustrative applications of constrained density functional
theory (DFT) to electron transfer dynamics in electronic materials. The kinetics of these
Vector Free Energy Calculation with Adaptive Biasing Force
18 Jun 2006 | Online Presentations | Contributor(s): Eric F Darve
This presentation discusses recent numerical methods to calculate the
free energy as a function of a reaction coordinate for bio-molecules.
Free energy is often called potential of mean force...
05 Jun 2006 | Online Presentations | Contributor(s): Dragica Vasileska
Molecular Dynamics Simulations with the Second-Generation Reactive Empirical Bond Order (REBO) Potential
02 Jun 2006 | Online Presentations | Contributor(s): Wen-Dung Hsu, Susan Sinnott
In this presentation, the molecular dynamics (MD) simulation will be introduced first. The applications of MD simulation, the procedure of MD simulation and some speed-up methods in MD simulation...
First Principles-Based Modeling of materials: Towards Computational Materials Design
20 Apr 2006 | Online Presentations | Contributor(s): Alejandro Strachan
Molecular dynamics (MD) simulations with accurate, first principles-based interatomic potentials is a powerful tool to uncover and characterize the molecular-level mechanisms that govern the...