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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.
Mechanical Properties of Surfactant Aggregates at Water-Solid Interfaces
0.0 out of 5 stars
05 Apr 2006 | Online Presentations | Contributor(s): Patrick Chiu, Kunal Shah, Susan Sinnott
This is a talk on the mechanical properties of surfactant
aggregates at water-solid interfaces using Micelle-MD. This
includes silica indentations of micelles with comparison to
Thermal Microsystems for On-Chip Thermal Engineering
04 Apr 2006 | Online Presentations | Contributor(s): Suresh V. Garimella
Electro-thermal co-design at the micro- and nano-scales is critical for
achieving desired performance and reliability in microelectronic circuits.
Emerging thermal microsystems technologies...
Molecular Transport Structures: Elastic Scattering, Vibronic Effects and Beyond
4.5 out of 5 stars
13 Feb 2006 | Online Presentations | Contributor(s): Mark A. Ratner, Abraham Nitzan, Misha Galperin
Current experimental efforts are clarifying quite beautifully the nature of charge transport in so-called molecular junctions, in which a single molecule provides the channel for current flow...
A Primer on Semiconductor Device Simulation
23 Jan 2006 | Online Presentations | Contributor(s): Mark Lundstrom
Computer simulation is now an essential tool for the research and development of semiconductor processes and devices, but to use a simulation
tool intelligently, one must know what's "under the...
Nano-Scale Device Simulations Using PROPHET-Part II: PDE Systems
5.0 out of 5 stars
22 Jan 2006 | Online Presentations | Contributor(s): Yang Liu, Robert Dutton
Part II uses examples to
illustrate how to build user-defined PDE systems in PROPHET.
Nano-Scale Device Simulations Using PROPHET-Part I: Basics
Part I covers the basics of PROPHET,
including the set-up of simulation structures and parameters based on
pre-defined PDE systems.
Nano-Scale Device Simulations Using PROPHET
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...
Hierarchical Physical Models for Analysis of Electrostatic Nanoelectromechanical Systems (NEMS)
05 Jan 2006 | Online Presentations | Contributor(s): Narayan Aluru
This talk will introduce hierarchical physical models and efficient
computational techniques for coupled analysis of electrical,
mechanical and van der Waals energy domains encountered in...
Quantum Corrections for Monte Carlo Simulation
05 Jan 2006 | Online Presentations | Contributor(s): Umberto Ravaioli
Size quantization is an important effect in modern scaled devices. Due to the cost and limitations of available full quantum approaches, it is appealing to extend semi-classical simulators by...
VolQD: Graphics Hardware Accelerated Interactive Visual Analytics of Multi-million Atom Nanoelectronics Simulations
21 Dec 2005 | Online Presentations | Contributor(s): Wei Qiao
In this work we present a hardware-accelerated direct volume rendering
system for visualizing multivariate wave functions in semiconducting
quantum dot (QD) simulations. The simulation...
First Principles-based Atomistic and Mesoscale Modeling of Materials
16 Nov 2005 | Online Presentations | Contributor(s): Alejandro Strachan
This tutorial will describe some of the most powerful and widely used techniques for materials modeling including i) first principles quantum mechanics (QM), ii) large-scale molecular dynamics...
Bandstructure in Nanoelectronics
01 Nov 2005 | Online Presentations | Contributor(s): Gerhard Klimeck
This presentation will highlight, for nanoelectronic device examples, how the effective mass approximation breaks down and why the quantum mechanical nature of the atomically resolved material...
Modeling and Simulation of Sub-Micron Thermal Transport
27 Sep 2005 | Online Presentations | Contributor(s): Jayathi Murthy
In recent years, there has been increasing interest in understanding thermal phenomena at the sub-micron scale. Applications include the thermal performance of microelectronic devices,...
26 Sep 2005 | Online Presentations | Contributor(s): Gerhard Klimeck
Quantum Dots are man-made artificial atoms that confine electrons to a small space. As such, they have atomic-like behavior and enable the study of quantum mechanical effects on a length scale...
Parallel Computing for Realistic Nanoelectronic Simulations
Typical modeling and simulation efforts directed towards the understanding of electron transport at the nanometer scale utilize single workstations as computational engines. Growing understanding...
Review of Several Quantum Solvers and Applications
29 Aug 2005 | Online Presentations | Contributor(s): Umberto Ravaioli
Numerical Aspects of NEGF: The Recursive Green Function Algorithm
20 Aug 2005 | Online Presentations | Contributor(s): Gerhard Klimeck
Computational Methods for NEMS
20 Aug 2005 | Online Presentations | Contributor(s): Narayan Aluru
Scientific Software Development
11 Aug 2005 | Online Presentations | Contributor(s): Clemens Heitzinger
The development of efficient scientific simulation codes poses a wide range of problems. How can we reduce the time spent in developing and debugging codes while still arriving at efficient...
NCN Cyberinfrastructure Overview
20 Jun 2005 | Online Presentations | Contributor(s): Gerhard Klimeck
Presentation of the NCN cyberinfrastructure to the June 2005 NSF review team. The nanoHUB development over 12 months will be presented in a broad overview.