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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.

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.

Online Presentations (1-20 of 77)

  1. A Primer on Semiconductor Device Simulation

    This resource has a 8.8 Ranking

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    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 …

    https://nanohub.org/resources/980

  2. An Introduction to Quantum Computing

    This resource has a 9.0 Ranking

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    Users: 1410
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    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 …

    https://nanohub.org/resources/4778

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

    This resource has a 7.0 Ranking

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    Users: 440
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    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 …

    https://nanohub.org/resources/1633

  4. Bandstructure in Nanoelectronics

    This resource has a 9.7 Ranking

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    Users: 4009
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    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 needs …

    https://nanohub.org/resources/381

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

    This resource has a 6.5 Ranking

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    Users: 225
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    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 upcoming …

    https://nanohub.org/resources/4717

  6. Calculating Resonances Using a Complex Absorbing Potential

    This resource has a 6.3 Ranking

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    Users: 288
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    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 …

    https://nanohub.org/resources/4143

  7. Challenges and Strategies for High End Computing

    This resource has a 8.9 Ranking

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    Users: 753
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    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 computational …

    https://nanohub.org/resources/3706

  8. Computational Mathematics: Role, Impact, Challenges

    This resource has a 6.7 Ranking

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    Users: 450
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    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 computational …

    https://nanohub.org/resources/3701

  9. Computational Methods for NEMS

    This resource has a 7.6 Ranking

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    Users: 897
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    16 Jun 2004 | Online Presentations | Contributor(s): Narayan Aluru

    Computational Methods for NEMS

    https://nanohub.org/resources/407

  10. Computing the Horribleness of Soft Condensed Matter

    This resource has a 8.0 Ranking

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    Users: 455
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    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 …

    https://nanohub.org/resources/3424

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

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    Users: 12
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    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 diverse …

    https://nanohub.org/resources/17535

  12. ECE 595E Lecture 35: MEEP Tutorial I

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

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

    https://nanohub.org/resources/17557

  13. ECE 595E Lecture 36: MEEP Tutorial II

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    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

    https://nanohub.org/resources/17558

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

    This resource has a 5.1 Ranking

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    Users: 74
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    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 …

    https://nanohub.org/resources/5910

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

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    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 …

    https://nanohub.org/resources/6856

  16. Exploring Electron Transfer with Density Functional Theory

    This resource has a 7.9 Ranking

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    11 Jun 2006 | Online Presentations | Contributor(s): Troy Van Voorhis

    This talk will highlight several illustrative applications of constrained density functional theory (DFT) to electron transfer dynamics in electronic materials. The kinetics of these reactions are …

    https://nanohub.org/resources/1566

  17. Exploring Physical and Chemical control of molecular conductance: A computational study

    This resource has a 5.8 Ranking

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    31 Jan 2008 | Online Presentations | Contributor(s): Barry D. Dunietz

    …

    https://nanohub.org/resources/3945

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

    This resource has a 9.8 Ranking

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    Users: 2166
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    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 (MD) …

    https://nanohub.org/resources/434

  19. First Principles-Based Modeling of materials: Towards Computational Materials Design

    This resource has a 7.2 Ranking

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    20 Apr 2006 | Online Presentations | Contributor(s): Alejandro Strachan

    Molecular dynamics (MD) simulations with accurate, first principles-based interatomic potentials is a powerful tool to uncover and characterize the molecular-level mechanisms that govern the …

    https://nanohub.org/resources/1239

  20. Hierarchical Physical Models for Analysis of Electrostatic Nanoelectromechanical Systems (NEMS)

    This resource has a 8.7 Ranking

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    Users: 922
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    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 …

    https://nanohub.org/resources/850

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