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.

Papers (1-2 of 2)

  1. Exploring New Channel Materials for Nanoscale CMOS

    21 May 2006 | Papers | Contributor(s): Anisur Rahman

    The improved transport properties of new channel materials, such as Ge and III-V semiconductors, along with new device designs, such as dual gate, tri gate or FinFETs, are expected to enhance the...

    http://nanohub.org/resources/1315

  2. Device Physics and Simulation of Silicon Nanowire Transistors

    20 May 2006 | Papers | 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