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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 184)

  1. 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

  2. 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

  3. 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

  4. 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

  5. ThrEshold Logic Synthesizer (TELS) and Majority Logic Synthezier (MALS)

    09 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

  6. 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

  7. 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

  8. MCW07 Electronic Level Alignment at Metal-Molecule Contacts with a GW Approach

    05 Sep 2007 | Online Presentations | Contributor(s): Jeffrey B. Neaton

    Most recent theoretical studies of electron transport in single-molecule junctions rely on a Landauer approach, simplified to treat electron-electron interactions at a mean-field level within...

    http://nanohub.org/resources/3094

  9. SUGAR: the SPICE for MEMS

    21 May 2007 | Online Presentations | Contributor(s): Jason Clark

    In this seminar, I present some design, modeling, and simulation features of a computer aided engineering tool for microelectromechanical systems (MEMS) called SUGAR. For experimental...

    http://nanohub.org/resources/2735

  10. Modeling and Analysis of VLSI Interconnects

    10 May 2007 | Online Presentations | Contributor(s): Cheng-Kok Koh

    With continual technology scaling, the accurate and efficient modeling and simulation of interconnect effects have become problems of central importance. In order to accurately model the...

    http://nanohub.org/resources/2698

  11. Renormalization Group Theories of Strongly Interacting Electronic Structure

    20 Apr 2007 | Online Presentations | Contributor(s): Garnet Chan, NCN SLC@Northwestern

    Our work is in the area of the electronic structure and dynamics of complex processes. We engage in developing new and more powerful theoretical techniques which enable us to describe strong...

    http://nanohub.org/resources/2616

  12. Is Seeing Believing? How to Think Visually and Analyze with Both Your Eyes and Brain

    26 Mar 2007 | Online Presentations | Contributor(s): David Ebert

    This presentation will cover the basic techniques, and some of the available tools, for visualization, and will explain how to avoid miscommunicating information from visualizations.

    http://nanohub.org/resources/2512

  13. Surprises on the nanoscale: Plasmonic waves that travel backward and spin birefringence without magnetic fields

    08 Jan 2007 | Online Presentations | Contributor(s): Daniel Neuhauser

    As nanonphotonics and nanoelectronics are pushed down towards the molecular scale, interesting effects emerge. We discuss how birefringence (different propagation of two polarizations) is...

    http://nanohub.org/resources/2256

  14. Computing Research Institute Seminars

    04 Jan 2007 | Series

    CRI sponsors a regular seminar series that features local, national and international speakers who are recognized in their fields. CRI seminars cover topics in computational science, computational...

    http://nanohub.org/resources/2166

  15. MOSCNT: code for carbon nanotube transistor simulation

    14 Nov 2006 | Downloads | Contributor(s): Siyu Koswatta, Jing Guo, Dmitri Nikonov

    Ballistic transport in carbon nanotube metal-oxide-semiconductor field-effect transistors (CNT-MOSFETs) is simulated using the Non-equilibrium Green’s function formalism. A cylindrical transistor...

    http://nanohub.org/resources/1989

  16. recursive algorithm for NEGF in Matlab

    13 Nov 2006 | Downloads | Contributor(s): Dmitri Nikonov, Siyu Koswatta

    This zip-archive contains two Matlab functions for the recursive solution of the partial matrix inversion and partial 3-matrix multiplication used in the non-equilibrium Green’s function (NEGF)...

    http://nanohub.org/resources/1983

  17. Understanding Phonon Dynamics via 1D Atomic Chains

    04 Apr 2006 | Online Presentations | Contributor(s): Timothy S Fisher

    Phonons are the principal carriers of thermal energy in semiconductors and insulators, and they serve a vital role in dissipating heat produced by scattered electrons in semiconductor devices....

    http://nanohub.org/resources/1186

  18. NEMO 3D: Intel optimizations and Multiple Quantum Dot Simulations

    03 Aug 2006 | Online Presentations | Contributor(s): Anish Dhanekula, Gerhard Klimeck

    NEMO-3D is a nanoelectronic modeling tool that analyzes the electronic structure of nanoscopic devices. Nanoelectronic devices such as Quantum Dots (QDs) can contain millions of atoms,. Therefore,...

    http://nanohub.org/resources/1673

  19. Autonomic Adaptation of Virtual Distributed Environments in a Multi-Domain Infrastructure

    11 Jul 2006 | Online Presentations | Contributor(s): Ryan Riley, Dongyan Xu

    By federating resources from multiple domains, a shared infrastructure provides aggregated computation resources to a large number of users. With rapid advances in virtualization technologies, we...

    http://nanohub.org/resources/1633

  20. Exploring Electron Transfer with Density Functional Theory

    11 Jun 2006 | Online Presentations | Contributor(s): Troy Van Voorhis

    This talk will highlight several illustrative applications of constrained density functional theory (DFT) to electron transfer dynamics in electronic materials. The kinetics of these reactions...

    http://nanohub.org/resources/1566

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