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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 (41-60 of 77)

  1. Renormalization Group Theories of Strongly Interacting Electronic Structure

    This resource has a 6.5 Ranking

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    20 Apr 2007 | Online Presentations | Contributor(s): Garnet Chan, NCN SLC@Northwestern

    Our work is in the area of the electronic structure and dynamics of complex processes. We engage in developing new and more powerful theoretical techniques which enable us to describe strong …

    https://nanohub.org/resources/2616

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

    This resource has a 10.0 Ranking

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    Users: 1172
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    26 Mar 2007 | Online Presentations | 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.

    https://nanohub.org/resources/2512

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

    This resource has a 9.1 Ranking

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    08 Jan 2007 | Online Presentations | 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 …

    https://nanohub.org/resources/2256

  4. Understanding Phonon Dynamics via 1D Atomic Chains

    This resource has a 10.0 Ranking

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    04 Apr 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. …

    https://nanohub.org/resources/1186

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

    This resource has a 7.4 Ranking

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    03 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, …

    https://nanohub.org/resources/1673

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

    This resource has a 7.0 Ranking

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    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 …

    https://nanohub.org/resources/1633

  7. Exploring Electron Transfer with Density Functional Theory

    This resource has a 7.9 Ranking

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    11 Jun 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 are …

    https://nanohub.org/resources/1566

  8. Vector Free Energy Calculation with Adaptive Biasing Force

    This resource has a 6.5 Ranking

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    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 and …

    https://nanohub.org/resources/1589

  9. Numerical Analysis

    This resource has a 10.0 Ranking

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

    https://nanohub.org/resources/1510

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

    This resource has a 6.1 Ranking

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    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 …

    https://nanohub.org/resources/1165

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

    This resource has a 7.2 Ranking

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    Users: 515
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    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 …

    https://nanohub.org/resources/1239

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

    This resource has a 9.9 Ranking

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    Users: 1137
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    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 …

    https://nanohub.org/resources/1214

  13. Tutorial on Using Micelle-MD

    This resource has a 6.6 Ranking

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    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 …

    https://nanohub.org/resources/1193

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

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    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 …

    https://nanohub.org/resources/1192

  15. Thermal Microsystems for On-Chip Thermal Engineering

    This resource has a 9.2 Ranking

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    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 for …

    https://nanohub.org/resources/1182

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

    This resource has a 8.6 Ranking

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    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 between …

    https://nanohub.org/resources/1018

  17. A Primer on Semiconductor Device Simulation

    This resource has a 8.8 Ranking

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    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 …

    https://nanohub.org/resources/980

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

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    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.

    https://nanohub.org/resources/975

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

    This resource has a 10.0 Ranking

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    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.

    https://nanohub.org/resources/974

  20. Nano-Scale Device Simulations Using PROPHET

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    Users: 2172
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    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 offers …

    https://nanohub.org/resources/973

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