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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.
An Introduction to Quantum Computing
5.0 out of 5 stars
12 Sep 2008 | Online Presentations | Contributor(s): Edward Gerjuoy
Quantum mechanics, as formulated more than 80 years ago by Schrodinger, Heisenberg, Dirac and other greats, is a wholly sufficient foundation for its modern interrelated subfields of quantum...
BNC Annual Research Review: An Introduction to PRISM and MEMS Simulation
0.0 out of 5 stars
04 Jun 2008 | Online Presentations | Contributor(s): Jayathi Murthy
This presentation is part of a collection of presentations describing the projects, people, and capabilities enhanced by research performed in the Birck Center, and a look at plans for the...
Calculating Resonances Using a Complex Absorbing Potential
14 Mar 2008 | Online Presentations | Contributor(s): Robin Santra
The Siegert (or Gamow) wave function associated with a resonance state is exponentially divergent at large distances from the scattering target. A complex absorbing potential (CAP) provides a...
Nanoelectronic Modeling: Multimillion Atom Simulations, Transport, and HPC Scaling to 23,000 Processors
07 Mar 2008 | Online Presentations | Contributor(s): Gerhard Klimeck
Future field effect transistors will be on the same length scales as “esoteric” devices such as quantum dots,
nanowires, ultra-scaled quantum wells, and resonant tunneling diodes. In those...
How to ensure that the stiffness matrix is square?
Closed | Responses: 1
Every time I run the solver, it stops giving an error that the stiffness matrix is not square (though it is symmetric). What should I do to ensure that the stiffness matrix is square so as to...
Gloria Wahyu Budiman
Exploring Physical and Chemical control of molecular conductance: A computational study
01 Feb 2008 | Online Presentations | Contributor(s): Barry D. Dunietz
Challenges and Strategies for High End Computing
20 Dec 2007 | Online Presentations | Contributor(s): Katherine A. Yelick
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...
NanoElectronic MOdeling: NEMO
20 Dec 2007 | Online Presentations | Contributor(s): Gerhard Klimeck
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...
Session 3: Discussion
20 Dec 2007 | Online Presentations
Discussion led by Jim Demmel, University of California at Berkeley.
Computational Mathematics: Role, Impact, Challenges
20 Dec 2007 | Online Presentations | Contributor(s): Juan C. Meza
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
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...
ThrEshold Logic Synthesizer (TELS) and Majority Logic Synthezier (MALS)
15 Oct 2007 | Downloads | Contributor(s): Pallav Gupta
TELS and MALS are threshold and majority/minority logic synthesis tools that were developed by Rui Zhang and Pallav Gupta under the supervision of Prof. Niraj K. Jha of Princeton University. Dr....
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...