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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 (61-80 of 184)

  1. Vector Free Energy Calculation with Adaptive Biasing Force

    18 Jun 2006 | Online Presentations | Contributor(s): Eric F Darve

    This presentation discusses recent numerical methods to calculate the free energy as a function of a reaction coordinate for bio-molecules. Free energy is often called potential of mean force...

    http://nanohub.org/resources/1589

  2. Numerical Analysis

    02 Jun 2006 | Online Presentations | Contributor(s): Dragica Vasileska

    http://nanohub.org/resources/1510

  3. Molecular Dynamics Simulations with the Second-Generation Reactive Empirical Bond Order (REBO) Potential

    02 Apr 2006 | Online Presentations | Contributor(s): Wen-Dung Hsu, Susan Sinnott

    In this presentation, the molecular dynamics (MD) simulation will be introduced first. The applications of MD simulation, the procedure of MD simulation and some speed-up methods in MD simulation...

    http://nanohub.org/resources/1165

  4. Exploring New Channel Materials for Nanoscale CMOS

    21 May 2006 | Publications | Contributor(s): Anisur Rahman

    The improved transport properties of new channel materials, such as Ge and III-V semiconductors, along with new device designs, such as dual gate, tri gate or FinFETs, are expected to enhance the...

    http://nanohub.org/resources/1315

  5. Device Physics and Simulation of Silicon Nanowire Transistors

    20 May 2006 | Publications | Contributor(s): Jing Wang

    As the conventional silicon metal-oxide-semiconductor field-effect transistor (MOSFET) approaches its scaling limits, many novel device structures are being extensively explored. Among them, the...

    http://nanohub.org/resources/1313

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

    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...

    http://nanohub.org/resources/1239

  7. The Long and Short of Pick-up Stick Transistors: A Promising Technology for Nano- and Macro-Electronics

    11 Apr 2006 | Online Presentations | Contributor(s): Muhammad A. Alam

    In recent years, there has been enormous interest in the emerging field of large-area macro-electronics, and fabricating thin-film transistors on flexible substrates. This talk will cover recent...

    http://nanohub.org/resources/1214

  8. Tutorial on Using Micelle-MD

    05 Apr 2006 | Online Presentations | Contributor(s): Patrick Chiu, Kunal Shah, Susan Sinnott

    This is a tutorial using Micelle-MD. This includes the main capabilities, computation procedure, with format of files generated, and the simulation setup, which includes the material models...

    http://nanohub.org/resources/1193

  9. Mechanical Properties of Surfactant Aggregates at Water-Solid Interfaces

    05 Apr 2006 | Online Presentations | Contributor(s): Patrick Chiu, Kunal Shah, Susan Sinnott

    This is a talk on the mechanical properties of surfactant aggregates at water-solid interfaces using Micelle-MD. This includes silica indentations of micelles with comparison to experimental...

    http://nanohub.org/resources/1192

  10. 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

  11. 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

  12. 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

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

    20 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

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

    20 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

  15. Nano-Scale Device Simulations Using PROPHET

    20 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

  16. 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

  17. 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

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

    13 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

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

    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...

    http://nanohub.org/resources/434

  20. 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

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