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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.
Illinois ECE 498AL: Programming Massively Parallel Processors, Lecture 12: Structuring Parallel Algorithms
15 Sep 2009 | Online Presentations | Contributor(s): Wen-Mei W Hwu
Structuring Parallel Algorithms
Key Parallel Programming Steps
Choosing Algorithm Structure
Mapping a Divide and Conquer algorithm
Experiment vs. Modelling: What's the problem?
10 Aug 2009 | Online Presentations | Contributor(s): William L. Barnes
Progress in plasmonics has been greatly assisted by developments in
experimental techniques and in numerical modelling. This talk will
look at some of the difficulties that emerge when...
Quantitative, Kinetic Models of Cellular Circuits
04 Apr 2009 | Online Presentations | Contributor(s): Michael R. Brent
Living cells contain complex, analog circuits that regulate the rate at which each gene produces its product. The kinetic properties of these circuits enable cells to respond to changes in their...
The Multicore Era: Crisis or (and?) Opportunity?
27 Mar 2009 | Online Presentations | Contributor(s): Mithuna Thottethodi
This talk will provide a brief overview of how we got to the multicore era, the implications and challenges for hardware/software developers and users, and some informed speculation on where the...
Experiences with nonintrusive polynomial Chaos and stochastic collocation methods for uncertainty analysis and design
0.0 out of 5 stars
13 Mar 2009 | Online Presentations | Contributor(s): Michael S. Eldred
Non—intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive
techniques for uncertainty quantification due to their abilities to produce functional...
Nanoparticle and Colloidal Simulations with Molecular Dynamics
05 Dec 2008 | Online Presentations | Contributor(s): Steve Plimpton
Modeling nanoparticle or colloidal systems in a molecular dynamics (MD) code requires coarse-graining on several levels to achieve meaningful simulation times for study of rheological and other...
25 Nov 2008 | Online Presentations | Contributor(s): Seung-Jai Min
This tutorial consists of three parts. First, we will discuss about
how OpenMP is typically used and explain OpenMP programming model. Second, we will describe important OpenMP constructs and...
Introduction to Parallel Programming with MPI
5.0 out of 5 stars
24 Nov 2008 | Online Presentations | Contributor(s): David Seaman
Single-session course illustrating message-passing techniques. The examples include point-to-point and collective communication using blocking and nonblocking transmission. One application...
Software Productivity Tools
This presentation briefly describes the use of tar(1), make(1), the
Portable Batch System (PBS), and two version control systems: CVS and subversion.
Introduction to TotalView
This single-session course presents an introduction to the use of the TotalView parallel debugger available on Purdue's Linux systems.
Quantum and Thermal Effects in Nanoscale Devices
4.5 out of 5 stars
18 Sep 2008 | Online Presentations | Contributor(s): Dragica Vasileska
To investigate lattice heating within a Monte Carlo device simulation framework, we simultaneously solve the Boltzmann transport equation for the electrons, the 2D Poisson equation to get the...
An Introduction to Quantum Computing
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
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...
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