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 (81-100 of 105)

  1. Thermal Microsystems for On-Chip Thermal Engineering

    04 Apr 2006 | Online Presentations | Contributor(s): Suresh V. Garimella

    Electro-thermal co-design at the micro- and nano-scales is critical for achieving desired performance and reliability in microelectronic circuits. Emerging thermal microsystems technologies...

    http://nanohub.org/resources/1182

  2. Molecular Transport Structures: Elastic Scattering, Vibronic Effects and Beyond

    13 Feb 2006 | Online Presentations | Contributor(s): Mark A. Ratner, Abraham Nitzan, Misha Galperin

    Current experimental efforts are clarifying quite beautifully the nature of charge transport in so-called molecular junctions, in which a single molecule provides the channel for current flow...

    http://nanohub.org/resources/1018

  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. Nano-Scale Device Simulations Using PROPHET-Part II: PDE Systems

    22 Jan 2006 | Online Presentations | Contributor(s): Yang Liu, Robert Dutton

    Part II uses examples to illustrate how to build user-defined PDE systems in PROPHET.

    http://nanohub.org/resources/975

  5. Nano-Scale Device Simulations Using PROPHET-Part I: Basics

    22 Jan 2006 | Online Presentations | Contributor(s): Yang Liu, Robert Dutton

    Part I covers the basics of PROPHET, including the set-up of simulation structures and parameters based on pre-defined PDE systems.

    http://nanohub.org/resources/974

  6. Nano-Scale Device Simulations Using PROPHET

    22 Jan 2006 | Online Presentations | Contributor(s): Yang Liu, Robert Dutton

    These two lectures are aimed to give a practical guide to the use of a general device simulator (PROPHET) available on nanoHUB. PROPHET is a partial differential equation (PDE) solver that...

    http://nanohub.org/resources/973

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

    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...

    http://nanohub.org/resources/850

  8. Quantum Corrections for Monte Carlo Simulation

    05 Jan 2006 | Online Presentations | Contributor(s): Umberto Ravaioli

    Size quantization is an important effect in modern scaled devices. Due to the cost and limitations of available full quantum approaches, it is appealing to extend semi-classical simulators by...

    http://nanohub.org/resources/847

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

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

    In this work we present a hardware-accelerated direct volume rendering system for visualizing multivariate wave functions in semiconducting quantum dot (QD) simulations. The simulation...

    http://nanohub.org/resources/789

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

    16 Nov 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...

    http://nanohub.org/resources/434

  11. 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

  12. Modeling and Simulation of Sub-Micron Thermal Transport

    27 Sep 2005 | Online Presentations | 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,...

    http://nanohub.org/resources/192

  13. Parallel Computing for Realistic Nanoelectronic Simulations

    26 Sep 2005 | Online Presentations | 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...

    http://nanohub.org/resources/191

  14. Quantum Dots

    26 Sep 2005 | Online Presentations | 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...

    http://nanohub.org/resources/189

  15. 2004 Computational Materials Science Summer School

    29 Aug 2005 | Workshops

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

    http://nanohub.org/resources/406

  16. Review of Several Quantum Solvers and Applications

    29 Aug 2005 | Online Presentations | Contributor(s): Umberto Ravaioli

    Review of Several Quantum Solvers and Applications

    http://nanohub.org/resources/413

  17. Computational Methods for NEMS

    20 Aug 2005 | Online Presentations | Contributor(s): Narayan Aluru

    Computational Methods for NEMS

    http://nanohub.org/resources/407

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

    20 Aug 2005 | Online Presentations | Contributor(s): Gerhard Klimeck

    Numerical Aspects of NEGF: The Recursive Green Function Algorithm

    http://nanohub.org/resources/165

  19. Scientific Software Development

    11 Aug 2005 | Online Presentations | 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...

    http://nanohub.org/resources/1041

  20. HPC and Visualization for multimillion atom simulations

    20 Jun 2005 | Online Presentations | 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.

    http://nanohub.org/resources/187