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.

Resources (81-100 of 135)

  1. Session 3: Discussion

    Online Presentations | 20 Dec 2007

    Discussion led by Jim Demmel, University of California at Berkeley.

  2. Computational Mathematics: Role, Impact, Challenges

    Online Presentations | 20 Dec 2007 | Contributor(s):: Juan C. Meza

    This presentation was one of 13 presentations in the one-day forum, "Excellence in Computer Simulation," which brought together a broad set of experts to reflect on the future of computational science and engineering.

  3. Hierarchical Temporal Memory: How a New Theory of Neocortex May Lead to Truly Intelligent Machines

    Online Presentations | 12 Dec 2007 | Contributor(s):: Jeff Hawkins

    Coaxing computers to perorm basic acts of perception and robotics, let alone high-level thought, has been difficult. No existing computer can recognize pictures, understand language, or navigate through a cluttered room with anywhere near a child's facility. Following nature's example, Jeff...

  4. HPCW Introduction to Parallel Programming with MPI

    Online Presentations | 05 Dec 2007 | Contributor(s):: David Seaman

    Single-session courseillustrating message-passing techniques. The examples include point-to-pointand collective communication using blocking and nonblocking transmission. Oneapplication illustrates the manager/worker model with buffered communications.Code examples provided in C, C++, Fortran 77,...

  5. Computing the Horribleness of Soft Condensed Matter

    Online Presentations | 19 Oct 2007 | Contributor(s):: Eric Jakobsson

    A great triumph of computer simulations 40 years ago was to make the liquid state of matter understandable in terms of physical interactions between individual molecules. Prior to the first simulations of liquid argon and liquid water in the 1960's, there was no quantitatively rigorous molecular...

  6. ThrEshold Logic Synthesizer (TELS) and Majority Logic Synthezier (MALS)

    Downloads | 09 Oct 2007 | Contributor(s):: Pallav Gupta

    TELS and MALS are threshold and majority/minority logic synthesis tools that were developed by Rui Zhang and Pallav Gupta under the supervision of Prof. Niraj K. Jha of Princeton University. Dr. Lin Zhong, of Rice University, was also a contributor.Both of these tools have been integrated into...

  7. HPCW Parallel Programming Models

    Online Presentations | 09 Oct 2007 | Contributor(s):: Sam Midkiff

  8. MCW07 Simple Models for Molecular Transport Junctions

    Online Presentations | 13 Sep 2007 | Contributor(s):: Misha Galperin, Abraham Nitzan, Mark Ratner

    We review our recent research on role of interactions in molecular transport junctions. We consider simple models within nonequilibrium Green function approach (NEGF) in steady-state regime.

  9. MCW07 Electronic Level Alignment at Metal-Molecule Contacts with a GW Approach

    Online Presentations | 05 Sep 2007 | Contributor(s):: Jeffrey B. Neaton

    Most recent theoretical studies of electron transport in single-molecule junctions rely on a Landauer approach, simplified to treat electron-electron interactions at a mean-field level within density functional theory (DFT). While this framework has proven relatively accurate for certain systems,...

  10. SUGAR: the SPICE for MEMS

    Online Presentations | 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...

  11. Modeling and Analysis of VLSI Interconnects

    Online Presentations | 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...

  12. Renormalization Group Theories of Strongly Interacting Electronic Structure

    Online Presentations | 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...

  13. 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.

  14. 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...

  15. Computing Research Institute Seminars

    Series | 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.

  16. MOSCNT: code for carbon nanotube transistor simulation

    Downloads | 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...

  17. recursive algorithm for NEGF in Matlab

    Downloads | 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...

  18. 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...

  19. 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...

  20. 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...