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 100)

  1. MOSCNT: code for carbon nanotube transistor simulation

    15 Nov 2006 | Downloads | Contributor(s): Siyu Koswatta, Jing Guo, Dmitri Nikonov

    Ballistic transport in carbon nanotube metal-oxide-semiconductor field-effect transistors (CNT-MOSFETs) is simulated using the Non-equilibrium Green’s function formalism. A cylindrical...

    http://nanohub.org/resources/1989

  2. recursive algorithm for NEGF in Matlab

    13 Nov 2006 | Downloads | Contributor(s): Dmitri Nikonov, Siyu Koswatta

    This zip-archive contains two Matlab functions for the recursive solution of the partial matrix inversion and partial 3-matrix multiplication used in the non-equilibrium Green’s function (NEGF)...

    http://nanohub.org/resources/1983

  3. Understanding Phonon Dynamics via 1D Atomic Chains

    28 Aug 2006 | Online Presentations | Contributor(s): Timothy S Fisher

    Phonons are the principal carriers of thermal energy in semiconductors and insulators, and they serve a vital role in dissipating heat produced by scattered electrons in semiconductor devices....

    http://nanohub.org/resources/1186

  4. NEMO 3D: Intel optimizations and Multiple Quantum Dot Simulations

    14 Aug 2006 | Online Presentations | Contributor(s): Anish Dhanekula, Gerhard Klimeck

    NEMO-3D is a nanoelectronic modeling tool that analyzes the electronic structure of nanoscopic devices. Nanoelectronic devices such as Quantum Dots (QDs) can contain millions of atoms,. Therefore,...

    http://nanohub.org/resources/1673

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

    11 Jul 2006 | Online Presentations | 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...

    http://nanohub.org/resources/1633

  6. Exploring Electron Transfer with Density Functional Theory

    03 Jul 2006 | Online Presentations | Contributor(s): Troy Van Voorhis

    This talk will highlight several illustrative applications of constrained density functional theory (DFT) to electron transfer dynamics in electronic materials. The kinetics of these reactions...

    http://nanohub.org/resources/1566

  7. 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

  8. Numerical Analysis

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

    http://nanohub.org/resources/1510

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

    02 Jun 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

  10. Exploring New Channel Materials for Nanoscale CMOS

    21 May 2006 | Papers | 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

  11. Device Physics and Simulation of Silicon Nanowire Transistors

    20 May 2006 | Papers | 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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