## 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.

### Online Presentations (1-20 of 86)

1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 16 Jun 2004 | | Contributor(s):: Narayan Aluru

Computational Methods for NEMS

12. 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. 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. 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. 18 Apr 2013 | | Contributor(s):: Peter Bermel

Outline:MEEP InterfacesMEEP ClassesTutorial examples:WaveguideBent waveguide

16. 30 Apr 2013 | | Contributor(s):: Peter Bermel

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

17. 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. 25 Jan 2017 | | Contributor(s):: Peter Bermel

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

19. 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. 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...