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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.

All Categories (1-20 of 184)

  1. 2004 Computational Materials Science Summer School

    07 Jun 2004 | Workshops

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

    http://nanohub.org/resources/406

  2. How to ensure that the stiffness matrix is square?

    Closed | Responses: 1

    Every time I run the solver, it stops giving an error that the stiffness matrix is not square (though it is symmetric). What should I do to ensure that the stiffness matrix is square so as to...

    http://nanohub.org/answers/question/49

  3. 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...

    http://nanohub.org/resources/980

  4. An Introduction to Quantum Computing

    12 Sep 2008 | Online Presentations | Contributor(s): Edward Gerjuoy

    Quantum mechanics, as formulated more than 80 years ago by Schrodinger, Heisenberg, Dirac and other greats, is a wholly sufficient foundation for its modern interrelated subfields of quantum...

    http://nanohub.org/resources/4778

  5. Autonomic Adaptation of Virtual Distributed Environments in a Multi-Domain Infrastructure

    11 Jul 2006 | Online Presentations | Contributor(s): Ryan Riley, Dongyan Xu

    By federating resources from multiple domains, a shared infrastructure provides aggregated computation resources to a large number of users. With rapid advances in virtualization technologies, we...

    http://nanohub.org/resources/1633

  6. 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

  7. BNC Annual Research Review: An Introduction to PRISM and MEMS Simulation

    04 Jun 2008 | Online Presentations | Contributor(s): Jayathi Murthy

    This presentation is part of a collection of presentations describing the projects, people, and capabilities enhanced by research performed in the Birck Center, and a look at plans for the...

    http://nanohub.org/resources/4717

  8. Calculating Resonances Using a Complex Absorbing Potential

    13 Mar 2008 | Online Presentations | Contributor(s): Robin Santra

    The Siegert (or Gamow) wave function associated with a resonance state is exponentially divergent at large distances from the scattering target. A complex absorbing potential (CAP) provides a...

    http://nanohub.org/resources/4143

  9. Challenges and Strategies for High End Computing

    20 Dec 2007 | Online Presentations | Contributor(s): Katherine A. Yelick

    This presentation was one of 13 presentations in the one-day forum, "Excellence in Computer Simulation," which brought together a broad set of experts to reflect on the future of...

    http://nanohub.org/resources/3706

  10. Computational Mathematics: Role, Impact, Challenges

    20 Dec 2007 | Online Presentations | Contributor(s): Juan C. Meza

    This presentation was one of 13 presentations in the one-day forum, "Excellence in Computer Simulation," which brought together a broad set of experts to reflect on the future of...

    http://nanohub.org/resources/3701

  11. Computational Methods for NEMS

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

    Computational Methods for NEMS

    http://nanohub.org/resources/407

  12. Computing Research Institute Seminars

    04 Jan 2007 | Series

    CRI sponsors a regular seminar series that features local, national and international speakers who are recognized in their fields. CRI seminars cover topics in computational science, computational...

    http://nanohub.org/resources/2166

  13. Computing the Horribleness of Soft Condensed Matter

    19 Oct 2007 | Online Presentations | Contributor(s): Eric Jakobsson

    A great triumph of computer simulations 40 years ago was to make the liquid state of matter understandable in terms of physical interactions between individual molecules. Prior to the first...

    http://nanohub.org/resources/3424

  14. Data-adaptive Filtering and the State of the Art in Image Processing

    15 Apr 2013 | Online Presentations | Contributor(s): Peyman Milanfar

    In this talk, I will present a practical and unified framework for understanding some common underpinnings of these methods. This leads to new insights and a broad understanding of how these...

    http://nanohub.org/resources/17535

  15. 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

  16. ECE 595 Course Policy - Spring 2013

    03 Jan 2013 | Teaching Materials | Contributor(s): Peter Bermel

    A description of the key policies that will govern the administration of ECE 595 on "Numerical Methods" in Spring 2013.

    http://nanohub.org/resources/16189

  17. ECE 595E Lecture 35: MEEP Tutorial I

    18 Apr 2013 | Online Presentations | Contributor(s): Peter Bermel

    Outline: MEEP Interfaces MEEP Classes Tutorial examples: Waveguide Bent waveguide

    http://nanohub.org/resources/17557

  18. ECE 595E Lecture 36: MEEP Tutorial II

    30 Apr 2013 | Online Presentations | Contributor(s): Peter Bermel

    Outline: Recap from Monday Examples Multimode ring resonators Isolating individual resonances Kerr nonlinearities Quantifying third-harmonic generation

    http://nanohub.org/resources/17558

  19. Experiences with nonintrusive polynomial Chaos and stochastic collocation methods for uncertainty analysis and design

    13 Mar 2009 | Online Presentations | Contributor(s): Michael S. Eldred

    Non—intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification due to their abilities to produce functional...

    http://nanohub.org/resources/5910

  20. Experiment vs. Modelling: What's the problem?

    10 Aug 2009 | Online Presentations | Contributor(s): William L. Barnes

    Progress in plasmonics has been greatly assisted by developments in experimental techniques and in numerical modelling. This talk will look at some of the difficulties that emerge when...

    http://nanohub.org/resources/6856

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