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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
out of 5 stars
29 Jun 2005 | | 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 programs? What happens when our codes must interact with existing tools? In recent years, higher-level...
NCN Cyberinfrastructure Overview
21 Jun 2005 | | 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
28 Dec 2004 | | 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, materials,medicine, biology and a variety of other areas will be developed in this new multi-disciplinary...
Scientific Computing with Python
24 Oct 2004 | | 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 CenterPython has emerged as an excellent choice for scientific computing because of its simple syntax, ease of use, and elegant multi-dimensional array arithmetic. Its interpreted evaluation...
Turbocharge Your Scientific Applications with Scripting
29 Apr 2004 | | 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 powerful tool with little extra effort by replacing the usual "main" program with an embedded scripting...