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 (81-100 of 115)

  1. Is Seeing Believing? How to Think Visually and Analyze with Both Your Eyes and Brain

    Online Presentations | 26 Mar 2007 | Contributor(s):: David Ebert

    This presentation will cover the basic techniques, and some of the available tools, for visualization, and will explain how to avoid miscommunicating information from visualizations.

  2. Surprises on the nanoscale: Plasmonic waves that travel backward and spin birefringence without magnetic fields

    Online Presentations | 08 Jan 2007 | Contributor(s):: Daniel Neuhauser

    As nanonphotonics and nanoelectronics are pushed down towards the molecular scale, interesting effects emerge. We discuss how birefringence (different propagation of two polarizations) is manifested and could be useful in the future for two systems: coherent plasmonic transport of near-field...

  3. Understanding Phonon Dynamics via 1D Atomic Chains

    Online Presentations | 04 Apr 2006 | 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. Despite the importance of phonons, rigorous understanding and inclusion of phonon dynamics in...

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

    Online Presentations | 03 Aug 2006 | 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, simulating their electronic structure, can take up to several days. In order to simulate and analyze...

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

    Online Presentations | 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. Exploring Electron Transfer with Density Functional Theory

    Online Presentations | 11 Jun 2006 | Contributor(s):: Troy Van Voorhis

    This talk will highlight several illustrative applications of constrained density functionaltheory (DFT) to electron transfer dynamics in electronic materials. The kinetics of thesereactions are commonly expressed in terms of well known Marcus parameters (drivingforce, reorganization energy and...

  7. Vector Free Energy Calculation with Adaptive Biasing Force

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

    This presentation discusses recent numerical methods to calculate thefree energy as a function of a reaction coordinate for bio-molecules.Free energy is often called potential of mean force and represents theeffective potential experienced by a generalized coordinate for abio-molecular system....

  8. Numerical Analysis

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

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

    Online Presentations | 02 Apr 2006 | 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 will be talked. Then the bond order potentials which are capable to predict bond breaking and new...

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

    Online Presentations | 20 Apr 2006 | 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 chemical, mechanical and optical properties of materials. Such fundamental understanding is critical to...

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

    Online Presentations | 11 Apr 2006 | 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 work in developing a comprehensive theoretical framework to describe the performance of these "pick-up...

  12. Tutorial on Using Micelle-MD

    Online Presentations | 05 Apr 2006 | 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 implemented.

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

    Online Presentations | 05 Apr 2006 | 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 data and graphite indentation of Micelle.

  14. Thermal Microsystems for On-Chip Thermal Engineering

    Online Presentations | 04 Apr 2006 | 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 for this application area are discussed, with specific examples including a novel micromechanical...

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

    Online Presentations | 13 Feb 2006 | Contributor(s):: Mark 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 between two electrodes. The theoretical modeling of such structures is challenging, because of the...

  16. A Primer on Semiconductor Device Simulation

    Online Presentations | 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...

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

    Online Presentations | 20 Jan 2006 | Contributor(s):: Yang Liu, Robert Dutton

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

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

    Online Presentations | 20 Jan 2006 | Contributor(s):: Yang Liu, Robert Dutton

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

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

    Online Presentations | 05 Jan 2006 | 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 Nanoelectromechanical Systems (NEMS). Numerical results will be presented for several silicon...

  20. Quantum Corrections for Monte Carlo Simulation

    Online Presentations | 05 Jan 2006 | 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 adding corrections for size quantization. Monte Carlo particle simulators are good candidates, because a...