Tags: algorithms

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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 (121-135 of 135)

  1. Bandstructure in Nanoelectronics

    4.5 out of 5 stars 

    Online Presentations | 01 Nov 2005 | 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 needs to be included in the device modeling. Atomistic bandstructure effects in resonant tunneling...

  2. Modeling and Simulation of Sub-Micron Thermal Transport

    0.0 out of 5 stars 

    Online Presentations | 26 Sep 2005 | 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, thermo-electric energy conversion, ultra-fast laser machining and many others. It is now accepted that Fourier's...

  3. Quantum Dots

    4.5 out of 5 stars 

    Online Presentations | 21 Jul 2005 | 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 that is around 100 times larger than the pure atomic scale. Quantum dots offer application...

  4. Parallel Computing for Realistic Nanoelectronic Simulations

    4.5 out of 5 stars 

    Online Presentations | 12 Sep 2005 | 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 of the involved physics and the need to model realistically extended devices increases the complexity...

  5. Review of Several Quantum Solvers and Applications

    4.5 out of 5 stars 

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

    Review of Several Quantum Solvers and Applications

  6. 2004 Computational Materials Science Summer School

    0.0 out of 5 stars 

    Workshops | 07 Jun 2004

    This short course will explore a range of computational approaches relevant for nanotechnology.

  7. Computational Methods for NEMS

    0.0 out of 5 stars 

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

    Computational Methods for NEMS

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

    0.0 out of 5 stars 

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

    Numerical Aspects of NEGF: The Recursive Green Function Algorithm

  9. Scientific Software Development

    5.0 out of 5 stars 

    Online Presentations | 29 Jun 2005 | 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 programs? What happens when our codes must interact with existing tools? In recent years, higher-level...

  10. NCN Cyberinfrastructure Overview

    0.0 out of 5 stars 

    Online Presentations | 21 Jun 2005 | 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.

  11. HPC and Visualization for multimillion atom simulations

    0.0 out of 5 stars 

    Online Presentations | 21 Jun 2005 | 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.

  12. MATLAB Scripts for "Quantum Transport: Atom to Transistor"

    4.0 out of 5 stars 

    Downloads | 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...

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

    0.0 out of 5 stars 

    Online Presentations | 28 Dec 2004 | 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, materials,medicine, biology and a variety of other areas will be developed in this new multi-disciplinary...

  14. Scientific Computing with Python

    5.0 out of 5 stars 

    Online Presentations | 24 Oct 2004 | 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 simple syntax, ease of use, and elegant multi-dimensional array arithmetic. Its interpreted...

  15. Turbocharge Your Scientific Applications with Scripting

    4.5 out of 5 stars 

    Online Presentations | 29 Apr 2004 | 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 powerful tool with little extra effort by replacing the usual "main" program with an embedded...