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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
out of 5 stars
20 Dec 2007 | | 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 computational science and engineering.
Hierarchical Temporal Memory: How a New Theory of Neocortex May Lead to Truly Intelligent Machines
12 Dec 2007 | | 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 through a cluttered room with anywhere near a child's facility. Following nature's example, Jeff...
HPCW Introduction to Parallel Programming with MPI
05 Dec 2007 | | Contributor(s):: David Seaman
Single-session courseillustrating message-passing techniques. The examples include point-to-pointand collective communication using blocking and nonblocking transmission. Oneapplication illustrates the manager/worker model with buffered communications.Code examples provided in C, C++, Fortran...
Computing the Horribleness of Soft Condensed Matter
19 Oct 2007 | | 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 simulations of liquid argon and liquid water in the 1960's, there was no quantitatively rigorous molecular...
HPCW Parallel Programming Models
09 Oct 2007 | | Contributor(s):: Sam Midkiff
MCW07 Simple Models for Molecular Transport Junctions
13 Sep 2007 | | Contributor(s):: , Abraham Nitzan, Mark 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 | | 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 density functional theory (DFT). While this framework has proven relatively accurate for certain...
SUGAR: the SPICE for MEMS
21 May 2007 | | 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 verification, I use a microdevice that is difficult to simulate with conventional MEMS software. I show that the...
Modeling and Analysis of VLSI Interconnects
10 May 2007 | | 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 distributive effects of interconnects, it is necessary to divide a long wire into several segments, with each...
Renormalization Group Theories of Strongly Interacting Electronic Structure
20 Apr 2007 | | Contributor(s):: Garnet Chan, NCN at Northwestern University
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 electronic correlation problems.Of particular theoretical interest are the construction of fast...
Is Seeing Believing? How to Think Visually and Analyze with Both Your Eyes and Brain
26 Mar 2007 | | Contributor(s)::
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
08 Jan 2007 | | Contributor(s)::
As nanonphotonics and nanoelectronics are pushed down towards the molecular scale, interesting effects emerge. We discuss how birefringence (different propagation of two polarizations) is manifested and could be useful in the future for two systems: coherent plasmonic transport of near-field...
Understanding Phonon Dynamics via 1D Atomic Chains
04 Apr 2006 | | 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. Despite the importance of phonons, rigorous understanding and inclusion of phonon dynamics in...
NEMO 3D: Intel optimizations and Multiple Quantum Dot Simulations
03 Aug 2006 | | 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, simulating their electronic structure, can take up to several days. In order to simulate and...
Autonomic Adaptation of Virtual Distributed Environments in a Multi-Domain Infrastructure
11 Jul 2006 | | 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 propose the concept of virtual distributed environments as a new sharing paradigm for a multi-domain...
Exploring Electron Transfer with Density Functional Theory
11 Jun 2006 | | Contributor(s)::
This talk will highlight several illustrative applications of constrained density functionaltheory (DFT) to electron transfer dynamics in electronic materials. The kinetics of thesereactions are commonly expressed in terms of well known Marcus parameters (drivingforce, reorganization energy and...
Vector Free Energy Calculation with Adaptive Biasing Force
18 Jun 2006 | | Contributor(s):: Eric F Darve
This presentation discusses recent numerical methods to calculate thefree energy as a function of a reaction coordinate for bio-molecules.Free energy is often called potential of mean force and represents theeffective potential experienced by a generalized coordinate for abio-molecular system....
02 Jun 2006 | | Contributor(s):: Dragica Vasileska
Molecular Dynamics Simulations with the Second-Generation Reactive Empirical Bond Order (REBO) Potential
02 Apr 2006 | | 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 will be talked. Then the bond order potentials which are capable to predict bond breaking and new...
First Principles-Based Modeling of materials: Towards Computational Materials Design
20 Apr 2006 | | 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 chemical, mechanical and optical properties of materials. Such fundamental understanding is critical to...