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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.

Resources (101-120 of 135)

  1. Exploring Electron Transfer with Density Functional Theory

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    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...

  2. Vector Free Energy Calculation with Adaptive Biasing Force

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    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....

  3. Numerical Analysis

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

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

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    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...

  5. Exploring New Channel Materials for Nanoscale CMOS

    4.5 out of 5 stars 

    Papers | 21 May 2006 | 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 performance of nanoscale CMOS devices.Novel process techniques, such as ALD, high-k dielectrics,...

  6. Device Physics and Simulation of Silicon Nanowire Transistors

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    Papers | 20 May 2006 | 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 silicon nanowire transistor (SNWT) has attracted broad attention from both the semiconductor industry...

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

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    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...

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

    5.0 out of 5 stars 

    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...

  9. Tutorial on Using Micelle-MD

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    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.

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

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    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.

  11. Thermal Microsystems for On-Chip Thermal Engineering

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    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...

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

    4.5 out of 5 stars 

    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...

  13. A Primer on Semiconductor Device Simulation

    4.5 out of 5 stars 

    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...

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

    5.0 out of 5 stars 

    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.

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

    5.0 out of 5 stars 

    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.

  16. Nano-Scale Device Simulations Using PROPHET

    5.0 out of 5 stars 

    Series | 20 Jan 2006 | 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 users the flexibility of integrating new models and equations for their nano-device simulations. The...

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

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    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...

  18. Quantum Corrections for Monte Carlo Simulation

    5.0 out of 5 stars 

    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...

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

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    Online Presentations | 13 Dec 2005 | Contributor(s):: Wei Qiao

    In this work we present a hardware-accelerated direct volume renderingsystem for visualizing multivariate wave functions in semiconductingquantum dot (QD) simulations. The simulation datacontains the probability density values of multiple electron orbitalsfor up to tens of millions of...

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

    5.0 out of 5 stars 

    Online Presentations | 01 Dec 2005 | 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 (MD) simulations and iii) mesoscale modeling, together with the strategies to bridge between them. These...