Tags: algorithms


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 (61-80 of 86)

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

    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...

  2. Tutorial on Using Micelle-MD

    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.

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

    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.

  4. Thermal Microsystems for On-Chip Thermal Engineering

    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...

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

    13 Feb 2006 | | Contributor(s):: Mark Ratner, Abraham Nitzan,

    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...

  6. A Primer on Semiconductor Device Simulation

    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 device simulation...

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

    20 Jan 2006 | | Contributor(s):: yang liu,

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

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

    20 Jan 2006 | | Contributor(s):: yang liu,

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

  9. Nano-Scale Device Simulations Using PROPHET

    20 Jan 2006 | | Contributor(s):: yang liu,

    These two lectures are aimed to give a practical guide to the use of ageneral device simulator (PROPHET) available on nanoHUB. PROPHETis a partial differential equation (PDE) solver that offers usersthe flexibility of integrating new models and equations for theirnano-device simulations. The...

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

    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...

  11. Quantum Corrections for Monte Carlo Simulation

    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...

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

    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 atoms,...

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

    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....

  14. Bandstructure in Nanoelectronics

    01 Nov 2005 | | 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 needs to be included in the device modeling. Atomistic bandstructure effects in resonant tunneling...

  15. Modeling and Simulation of Sub-Micron Thermal Transport

    26 Sep 2005 | | Contributor(s):: Jayathi Murthy

    In recent years, there has been increasing interest in understanding thermal phenomena at the sub-micron scale. Applications include the thermal performance of microelectronic devices, thermo-electric energy conversion, ultra-fast laser machining and many others. It is now accepted that...

  16. Quantum Dots

    21 Jul 2005 | | Contributor(s):: Gerhard Klimeck

    Quantum Dots are man-made artificial atoms that confine electrons to a small space. As such, they have atomic-like behavior and enable the study of quantum mechanical effects on a length scale that is around 100 times larger than the pure atomic scale. Quantum dots offer application...

  17. Parallel Computing for Realistic Nanoelectronic Simulations

    12 Sep 2005 | | Contributor(s):: Gerhard Klimeck

    Typical modeling and simulation efforts directed towards the understanding of electron transport at the nanometer scale utilize single workstations as computational engines. Growing understanding of the involved physics and the need to model realistically extended devices increases the...

  18. Review of Several Quantum Solvers and Applications

    11 Jun 2004 | | Contributor(s):: Umberto Ravaioli

    Review of Several Quantum Solvers and Applications

  19. Numerical Aspects of NEGF: The Recursive Green Function Algorithm

    14 Jun 2004 | | Contributor(s):: Gerhard Klimeck

    Numerical Aspects of NEGF: The Recursive Green Function Algorithm

  20. Computational Methods for NEMS

    16 Jun 2004 | | Contributor(s):: Narayan Aluru

    Computational Methods for NEMS