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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.
Ax = f
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.
MATLAB Scripts for "Quantum Transport: Atom to Transistor"
out of 5 stars
15 Mar 2005 | | Contributor(s):: Supriyo Datta
Tinker with quantum transport models! Download the MATLAB scripts used to demonstrate the physics described in Supriyo Datta's book Quantum Transport: Atom to Transistor. These simple models are less than a page of code, and yet they reproduce much of the fundamental physics observed in...
MOSCNT: code for carbon nanotube transistor simulation
14 Nov 2006 | | 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 geometry with wrapped-around gate and doped source/drain regions are assumed. It should be noted...
recursive algorithm for NEGF in Matlab
13 Nov 2006 | | 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) method.recuresealg3d.m- works for 3-diagonal matricesrecuresealgblock3d.m- works for 3-block-diagonal...
ThrEshold Logic Synthesizer (TELS) and Majority Logic Synthezier (MALS)
09 Oct 2007 | | 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. Lin Zhong, of Rice University, was also a contributor.Both of these tools have been integrated into...