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 (41-60 of 107)

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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...

    http://nanohub.org/resources/4143

  7. 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

  8. 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

  9. Gloria Wahyu Budiman

    http://nanohub.org/members/26820

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

    01 Feb 2008 | Online Presentations | Contributor(s): Barry D. Dunietz

    http://nanohub.org/resources/3945

  11. 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...

    http://nanohub.org/resources/3706

  12. 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...

    http://nanohub.org/resources/3707

  13. Session 3: Discussion

    20 Dec 2007 | Online Presentations

    Discussion led by Jim Demmel, University of California at Berkeley.

    http://nanohub.org/resources/3734

  14. Computational Mathematics: Role, Impact, Challenges

    20 Dec 2007 | Online Presentations | Contributor(s): Juan C. Meza

    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...

    http://nanohub.org/resources/3701

  15. 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...

    http://nanohub.org/resources/3555

  16. HPCW Introduction to Parallel Programming with MPI

    05 Dec 2007 | 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/3357

  17. 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...

    http://nanohub.org/resources/3424

  18. 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....

    http://nanohub.org/resources/3353

  19. HPCW Parallel Programming Models

    09 Oct 2007 | Online Presentations | Contributor(s): Sam Midkiff

    Computing Research Institute Rosen Center for Advanced Computing

    http://nanohub.org/resources/3341

  20. 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.

    http://nanohub.org/resources/3072