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.

Online Presentations (1-20 of 86)

  1. A Distributed Algorithm for Computing a Common Fixed Point of a Family of Paracontractions

    21 Jun 2017 | | Contributor(s):: A. Stephen Morse

    In this talk a distributed algorithm is described for finding a common fixed point of a family of m paracontractions assuming that such a common fixed point exists. The common fixed point is simultaneously computed by m agents assuming each agent knows only paracontraction, the current estimates...

  2. A Primer on Semiconductor Device Simulation

    23 Jan 2006 | | 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 hood." This talk is a tutorial introduction designed for someone using semiconductor device simulation...

  3. A Scalable Algorithm for Inverse Medium Problems with Multiple Sources

    02 Feb 2016 | | Contributor(s):: Keith Kelly

    We consider the problem of acoustic scattering as described by the free-space, time-harmonic scalar wave equation given by   (0.1)   along with radiation boundary conditions. Here, is a point in , is the source term, and is the wavenumber. Our formulation is based on potential theory....

  4. An Introduction to Quantum Computing

    12 Sep 2008 | | 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 computation (qc) and quantum information (qi), which generally are lumped together into a single subfield...

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

    11 Jul 2006 | | 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 propose the concept of virtual distributed environments as a new sharing paradigm for a multi-domain...

  6. Bandstructure in Nanoelectronics

    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...

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

    04 Jun 2008 | | 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 year.

  8. Calculating Resonances Using a Complex Absorbing Potential

    13 Mar 2008 | | 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 computationally simple and efficient technique for calculating the complex Siegert energy of a resonance...

  9. Challenges and Strategies for High End Computing

    20 Dec 2007 | | 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 science and engineering.

  10. Computational Mathematics: Role, Impact, Challenges

    20 Dec 2007 | | 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 science and engineering.

  11. Computational Methods for NEMS

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

    Computational Methods for NEMS

  12. Computing the Horribleness of Soft Condensed Matter

    19 Oct 2007 | | 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 simulations of liquid argon and liquid water in the 1960's, there was no quantitatively rigorous molecular...

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

    15 Apr 2013 | | 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 methods interrelate. I will also discuss the statistical performance of the resulting algorithms,...

  14. Data-Centric Models for Multilevel Algorithms

    07 Feb 2016 | | Contributor(s):: Samuel Guiterrez

    Today, computational scientists must contend with a diverse set of supercomputer architectures that are capable of exposing unprecedented levels of parallelism and complexity. Effectively placing, moving, and operating on data residing in complex distributed memory hierarchies is quickly...

  15. ECE 595E Lecture 35: MEEP Tutorial I

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

    Outline:MEEP InterfacesMEEP ClassesTutorial examples:WaveguideBent waveguide

  16. ECE 595E Lecture 36: MEEP Tutorial II

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

    Outline:Recap from MondayExamplesMultimode ring resonatorsIsolating individual resonancesKerr nonlinearitiesQuantifying third-harmonic generation

  17. ECE 695NS Lecture 2: Computability and NP-hardness

    13 Jan 2017 | | Contributor(s):: Peter Bermel

    Outline:OverviewDefinitionsComputing MachinesChurch-Turing ThesisPolynomial Time (Class P)Class NPNon-deterministic Turing machinesReducibilityCook-Levin theoremCoping with NP Hardness

  18. ECE 695NS Lecture 3: Practical Assessment of Code Performance

    25 Jan 2017 | | Contributor(s):: Peter Bermel

    Outline:Time ScalingExamplesGeneral performance strategiesComputer architecturesMeasuring code speedReduce strengthMinimize array writesProfiling

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

    13 Mar 2009 | | 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 representations of stochastic variability and to achieve exponential convergence rates in statistics of...

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

    10 Aug 2009 | | 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 comparisons are made between experiment and theory. Through the use of four examples I will illustrate what...