Tags: algorithms

Description

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.

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.

All Categories (21-40 of 97)

  1. Illinois ECE 498AL: Programming Massively Parallel Processors, Lecture 13: Reductions and their Implementation

    15 Sep 2009 | Online Presentations | Contributor(s): Wen-Mei W Hwu

    Structuring Parallel Algorithms Topics: Parallel Reductions Parallel Prefix Sum Relevance of Scan Application of Scan Scan on the CPU First attempt Parallel Scan Algorithm Work...

    http://nanohub.org/resources/7376

  2. 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 Topics: Key Parallel Programming Steps Algorithms Choosing Algorithm Structure Mapping a Divide and Conquer algorithm Tiled Algorithms Increased work...

    http://nanohub.org/resources/7372

  3. 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...

    http://nanohub.org/resources/6856

  4. 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...

    http://nanohub.org/resources/6374

  5. 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...

    http://nanohub.org/resources/6523

  6. Experiences with nonintrusive polynomial Chaos and stochastic collocation methods for uncertainty analysis and design

    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...

    http://nanohub.org/resources/5910

  7. 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...

    http://nanohub.org/resources/5668

  8. OpenMP Tutorial

    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...

    http://nanohub.org/resources/5874

  9. Purdue School on High Performance and Parallel Computing

    24 Nov 2008 | Workshops | Contributor(s): Alejandro Strachan, Faisal Saied

    The goal of this workshop is to provide training in the area of high performance scientific computing for graduate students and researchers interested in scientific computing. The School will...

    http://nanohub.org/resources/5666

  10. Introduction to Parallel Programming with MPI

    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...

    http://nanohub.org/resources/5932

  11. Software Productivity Tools

    24 Nov 2008 | Online Presentations | Contributor(s): David Seaman

    This presentation briefly describes the use of tar(1), make(1), the Portable Batch System (PBS), and two version control systems: CVS and subversion.

    http://nanohub.org/resources/5937

  12. Introduction to TotalView

    24 Nov 2008 | Online Presentations | Contributor(s): David Seaman

    This single-session course presents an introduction to the use of the TotalView parallel debugger available on Purdue's Linux systems.

    http://nanohub.org/resources/5942

  13. Quantum and Thermal Effects in Nanoscale Devices

    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...

    http://nanohub.org/resources/5448

  14. 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...

    http://nanohub.org/resources/4778

  15. 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...

    http://nanohub.org/resources/4717

  16. Calculating Resonances Using a Complex Absorbing Potential

    13 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...

    http://nanohub.org/resources/4143

  17. 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...

    http://nanohub.org/resources/3988

  18. 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...

    http://nanohub.org/answers/question/49

  19. Gloria Wahyu Budiman

    http://nanohub.org/members/26820

  20. Exploring Physical and Chemical control of molecular conductance: A computational study

    31 Jan 2008 | Online Presentations | Contributor(s): Barry D. Dunietz

    http://nanohub.org/resources/3945