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 (101-115 of 115)

  1. VolQD: Graphics Hardware Accelerated Interactive Visual Analytics of Multi-million Atom Nanoelectronics Simulations

    Online Presentations | 13 Dec 2005 | Contributor(s):: Wei Qiao

    In this work we present a hardware-accelerated direct volume renderingsystem for visualizing multivariate wave functions in semiconductingquantum dot (QD) simulations. The simulation datacontains the probability density values of multiple electron orbitalsfor up to tens of millions of...

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

    Online Presentations | 01 Dec 2005 | 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) simulations and iii) mesoscale modeling, together with the strategies to bridge between them. These...

  3. Bandstructure in Nanoelectronics

    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...

  4. Modeling and Simulation of Sub-Micron Thermal Transport

    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...

  5. Quantum Dots

    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...

  6. Parallel Computing for Realistic Nanoelectronic Simulations

    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...

  7. Review of Several Quantum Solvers and Applications

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

    Review of Several Quantum Solvers and Applications

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

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

    Numerical Aspects of NEGF: The Recursive Green Function Algorithm

  9. Computational Methods for NEMS

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

    Computational Methods for NEMS

  10. Scientific Software Development

    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...

  11. HPC and Visualization for multimillion atom simulations

    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. NCN Cyberinfrastructure Overview

    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.

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

    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

    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

    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...