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 (101-120 of 146)

  1. SUGAR: the SPICE for MEMS

    21 May 2007 | | Contributor(s):: Jason Clark

    In this seminar, I present some design, modeling, and simulation features of a computer aided engineering tool for microelectromechanical systems (MEMS) called SUGAR. For experimental verification, I use a microdevice that is difficult to simulate with conventional MEMS software. I show that...

  2. Modeling and Analysis of VLSI Interconnects

    10 May 2007 | | Contributor(s):: Cheng-Kok Koh

    With continual technology scaling, the accurate and efficient modeling and simulation of interconnect effects have become problems of central importance. In order to accurately model the distributive effects of interconnects, it is necessary to divide a long wire into several segments, with each...

  3. Renormalization Group Theories of Strongly Interacting Electronic Structure

    20 Apr 2007 | | Contributor(s):: Garnet Chan, NCN at Northwestern University

    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 electronic correlation problems.Of particular theoretical interest are the construction of fast...

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

    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.

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

    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...

  6. Computing Research Institute Seminars

    04 Jan 2007 |

    CRI sponsors a regular seminar series that features local, national and international speakers who are recognized in their fields. CRI seminars cover topics in computational science, computational life science, computer systems technology, and nano-computation.

  7. MOSCNT: code for carbon nanotube transistor simulation

    14 Nov 2006 | | 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 transistor geometry with wrapped-around gate and doped source/drain regions are assumed. It should be noted that...

  8. recursive algorithm for NEGF in Matlab

    13 Nov 2006 | | 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) method.recuresealg3d.m- works for 3-diagonal matricesrecuresealgblock3d.m- works for 3-block-diagonal...

  9. Understanding Phonon Dynamics via 1D Atomic Chains

    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...

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

    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...

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

    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...

  12. Exploring Electron Transfer with Density Functional Theory

    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...

  13. Vector Free Energy Calculation with Adaptive Biasing Force

    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....

  14. Numerical Analysis

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

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

    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...

  16. Exploring New Channel Materials for Nanoscale CMOS

    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,...

  17. Device Physics and Simulation of Silicon Nanowire Transistors

    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...

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

    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...

  19. 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 "pick-up...

  20. 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.