Support

Trouble Report

For immediate assistance browse through our Knowledge Base. You can find answers to many questions in just a few minutes.

Have a feature request? Try our Wish List!

If still experiencing problems, send us a report.

required
Why the math question?
 
You are here: Tags › algorithms › All Categories

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.

Questions & Answers 1 result (feed)

  1. 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 run the …

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

Total 1 results found.

Resources 80 results (feed)

  1. Scientific Computing with Python

    This resource has a 10.0 Ranking

    Ranking is calculated from a formula comprised of user reviews and usage data. Learn more ›

    Usage Stats
    Total: updated 01 Jan, 2010
    Users: 2554
    Reviews & Citations
    Google/IEEE
    Avg. Review: 5.0 out of 5 stars
    Citations:

    24 Oct 2004 | Online Presentations | Contributor(s): Eric Jones, Travis Oliphant

    Python 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 allows it to …

    http://nanohub.org/resources/99

  2. Nano-Scale Device Simulations Using PROPHET

    This resource has a 10.0 Ranking

    Ranking is calculated from a formula comprised of user reviews and usage data. Learn more ›

    Usage Stats
    Total: updated 01 Jan, 2010
    Users: 1617
    Reviews & Citations
    Google/IEEE
    Avg. Review: 5.0 out of 5 stars
    Citations:

    20 Jan 2006 | Online Presentations | Contributor(s): Yang Liu, Robert Dutton

    These two lectures are aimed to give a practical guide to the use of a general device simulator (PROPHET) available on nanoHUB. PROPHET is a partial differential equation (PDE) solver that offers …

    http://nanohub.org/resources/973

  3. Nano-Scale Device Simulations Using PROPHET-Part I: Basics

    This resource has a 10.0 Ranking

    Ranking is calculated from a formula comprised of user reviews and usage data. Learn more ›

    Usage Stats
    Total: updated 01 Jan, 2010
    Users: 1189
    Reviews & Citations
    Google/IEEE
    Avg. Review: 5.0 out of 5 stars
    Citations:

    20 Jan 2006 | Online Presentations | Contributor(s): Yang Liu, Robert Dutton

    Part I covers the basics of PROPHET, including the set-up of simulation structures and parameters based on pre-defined PDE systems.

    http://nanohub.org/resources/974

  4. Understanding Phonon Dynamics via 1D Atomic Chains

    This resource has a 10.0 Ranking

    Ranking is calculated from a formula comprised of user reviews and usage data. Learn more ›

    Usage Stats
    Total: updated 01 Jan, 2010
    Users: 1092
    Reviews & Citations
    Google/IEEE
    Avg. Review: 0.0 out of 5 stars
    Citations:

    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

  5. Device Physics and Simulation of Silicon Nanowire Transistors

    This resource has a 10.0 Ranking

    Ranking is calculated from a formula comprised of user reviews and usage data. Learn more ›

    Usage Stats
    Total: updated 01 Jan, 2010
    Users: 934
    Reviews & Citations
    Google/IEEE
    Avg. Review: 0.0 out of 5 stars
    Citations:

    20 May 2006 | Publications | Contributor(s): Jing Wang

    As the conventional silicon metal-oxide-semiconductor field-effect transistor (MOSFET) approaches its scaling limits, many novel device structures are being extensively explored. Among them, the …

    http://nanohub.org/resources/1313

Total 5 results found. | See more results

Members 1 result (feed)

  1. Gloria Wahyu Budiman

    http://nanohub.org/members/26820

Total 1 results found.

Get Help

Get Involved

Legal

nanoHUB.org is supported by the National Science Foundation and other funding agencies.