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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.

Resources (61-80 of 90)

  1. 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...

    http://nanohub.org/resources/847

  2. VolQD: Graphics Hardware Accelerated Interactive Visual Analytics of Multi-million Atom Nanoelectronics Simulations

    13 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...

    http://nanohub.org/resources/789

  3. First Principles-based Atomistic and Mesoscale Modeling of Materials

    01 Dec 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...

    http://nanohub.org/resources/434

  4. 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...

    http://nanohub.org/resources/381

  5. Modeling and Simulation of Sub-Micron Thermal Transport

    26 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,...

    http://nanohub.org/resources/192

  6. Quantum Dots

    21 Jul 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...

    http://nanohub.org/resources/189

  7. Parallel Computing for Realistic Nanoelectronic Simulations

    12 Sep 2005 | Online Presentations | Contributor(s): Gerhard Klimeck

    Typical modeling and simulation efforts directed towards the understanding of electron transport at the nanometer scale utilize single workstations as computational engines. Growing understanding...

    http://nanohub.org/resources/191

  8. Review of Several Quantum Solvers and Applications

    11 Jun 2004 | Online Presentations | Contributor(s): Umberto Ravaioli

    Review of Several Quantum Solvers and Applications

    http://nanohub.org/resources/413

  9. Numerical Aspects of NEGF: The Recursive Green Function Algorithm

    14 Jun 2004 | Online Presentations | Contributor(s): Gerhard Klimeck

    Numerical Aspects of NEGF: The Recursive Green Function Algorithm

    http://nanohub.org/resources/165

  10. Computational Methods for NEMS

    16 Jun 2004 | Online Presentations | Contributor(s): Narayan Aluru

    Computational Methods for NEMS

    http://nanohub.org/resources/407

  11. Scientific Software Development

    29 Jun 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...

    http://nanohub.org/resources/1041

  12. NCN Cyberinfrastructure Overview

    21 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.

    http://nanohub.org/resources/186

  13. HPC and Visualization for multimillion atom simulations

    21 Jun 2005 | Online Presentations | Contributor(s): Gerhard Klimeck

    This presentation gives an overview of the HPC and visulaization efforts involving multi-million atom simulations for the June 2005 NSF site visit to the Network for Computational Nanotechnology.

    http://nanohub.org/resources/187

  14. NEMO 1-D: The First NEGF-based TCAD Tool and Network for Computational Nanotechnology

    28 Dec 2004 | Online Presentations | Contributor(s): Gerhard Klimeck

    Nanotechnology has received a lot of public attention since U.S. President Clinton announced the U.S. National Nanotechnology Initiative. New approaches to applications in electronics,...

    http://nanohub.org/resources/178

  15. Scientific Computing with Python

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

    INSTRUCTORS: Eric Jones and Travis Oliphant. Sunday, October 24, 9:00 a.m. - 5:00 p.m. Room 322, Stewart Center Python has emerged as an excellent choice for scientific computing because of its...

    http://nanohub.org/resources/99

  16. Turbocharge Your Scientific Applications with Scripting

    29 Apr 2004 | Online Presentations | Contributor(s): Michael McLennan

    Scientific applications are built with great care and attention to the core simulation algorithms, often with some input/output added as an afterthought. Instead, you can create a much more...

    http://nanohub.org/resources/164

nanoHUB.org, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.