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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.
Scientific Software Development
0.0 out of 5 stars
11 Aug 2005 | Online Presentations | Contributor(s): Clemens Heitzinger
The development of efficient scientific simulation codes poses a wide range of problems. How can we reduce the time spent in developing and debugging codes while still arriving at efficient...
NCN Cyberinfrastructure Overview
20 Jun 2005 | Online Presentations | Contributor(s): Gerhard Klimeck
Presentation of the NCN cyberinfrastructure to the June 2005 NSF review team. The nanoHUB development over 12 months will be presented in a broad overview.
HPC and Visualization for multimillion atom simulations
This presentation gives an overview of the HPC and visulaization efforts involving multi-million atom simulations for the June 2005 NSF site visit to the Network for Computational Nanotechnology.
NEMO 1-D: The First NEGF-based TCAD Tool and Network for Computational Nanotechnology
04 Nov 2004 | Online Presentations | Contributor(s): Gerhard Klimeck
Nanotechnology has received a lot of public attention since U.S. President Clinton announced the U.S.
National Nanotechnology Initiative. New approaches to applications in electronics,...
Scientific Computing with Python
5.0 out of 5 stars
24 Oct 2004 | Online Presentations | Contributor(s): Eric Jones, Travis Oliphant
INSTRUCTORS: Eric Jones and Travis Oliphant.
Sunday, October 24, 9:00 a.m. - 5:00 p.m.
Room 322, Stewart Center
Python has emerged as an excellent choice for scientific computing because of its...
Turbocharge Your Scientific Applications with Scripting
4.5 out of 5 stars
14 Sep 2004 | Online Presentations | Contributor(s): Michael McLennan
Scientific applications are built with great care and attention to the core simulation algorithms, often with some input/output added as an afterthought. Instead, you can create a much more...