Tags: algorithms

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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.

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  1. Introduction to TotalView

    out of 5 stars 

    24 Nov 2008 | | Contributor(s):: David Seaman

    This single-session course presents an introduction to the use of the TotalView parallel debugger available on Purdue's Linux systems.

  2. Quantum and Thermal Effects in Nanoscale Devices

    out of 5 stars 

    18 Sep 2008 | | Contributor(s):: Dragica Vasileska

    To investigate lattice heating within a Monte Carlo device simulation framework, we simultaneously solve the Boltzmann transport equation for the electrons, the 2D Poisson equation to get the self-consistent fields and the hydrodynamic equations for acoustic and optical phonons. The phonon...

  3. An Introduction to Quantum Computing

    out of 5 stars 

    12 Sep 2008 | | Contributor(s):: Edward Gerjuoy

    Quantum mechanics, as formulated more than 80 years ago by Schrodinger, Heisenberg, Dirac and other greats, is a wholly sufficient foundation for its modern interrelated subfields of quantum computation (qc) and quantum information (qi), which generally are lumped together into a single subfield...

  4. BNC Annual Research Review: An Introduction to PRISM and MEMS Simulation

    out of 5 stars 

    04 Jun 2008 | | Contributor(s):: Jayathi Murthy

    This presentation is part of a collection of presentations describing the projects, people, and capabilities enhanced by research performed in the Birck Center, and a look at plans for the upcoming year.

  5. Calculating Resonances Using a Complex Absorbing Potential

    out of 5 stars 

    13 Mar 2008 | | Contributor(s):: Robin Santra

    The Siegert (or Gamow) wave function associated with a resonance state is exponentially divergent at large distances from the scattering target. A complex absorbing potential (CAP) provides a computationally simple and efficient technique for calculating the complex Siegert energy of a resonance...

  6. Nanoelectronic Modeling: Multimillion Atom Simulations, Transport, and HPC Scaling to 23,000 Processors

    out of 5 stars 

    07 Mar 2008 | | Contributor(s):: Gerhard Klimeck

    Future field effect transistors will be on the same length scales as “esoteric” devices such as quantum dots, nanowires, ultra-scaled quantum wells, and resonant tunneling diodes. In those structures the behavior of carriers and their interaction with their environment need to be fundamentally...

  7. How to ensure that the stiffness matrix is square?

    Q&A|Closed | Responses: 1

    Every time I run the solver, it stops giving an error that the stiffness matrix is not square (though it is symmetric). What should I do to ensure that the stiffness matrix is square so as to...

    https://nanohub.org/answers/question/49

  8. Gloria Wahyu Budiman

    https://nanohub.org/members/26820

  9. Exploring Physical and Chemical control of molecular conductance: A computational study

    out of 5 stars 

    31 Jan 2008 | | Contributor(s):: Barry D. Dunietz

  10. Challenges and Strategies for High End Computing

    out of 5 stars 

    20 Dec 2007 | | Contributor(s):: Katherine A. Yelick

    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.

  11. NanoElectronic MOdeling: NEMO

    out of 5 stars 

    20 Dec 2007 | | Contributor(s):: Gerhard Klimeck

    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.Novel nanoelectronic devices such as quantum dots, nanowires, and ultra-scaled...

  12. Session 3: Discussion

    out of 5 stars 

    20 Dec 2007 |

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

  13. Computational Mathematics: Role, Impact, Challenges

    out of 5 stars 

    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.

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

    out of 5 stars 

    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...

  15. HPCW Introduction to Parallel Programming with MPI

    out of 5 stars 

    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,...

  16. Computing the Horribleness of Soft Condensed Matter

    out of 5 stars 

    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...

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

    out of 5 stars 

    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...

  18. HPCW Parallel Programming Models

    out of 5 stars 

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

  19. MCW07 Simple Models for Molecular Transport Junctions

    out of 5 stars 

    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.

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

    out of 5 stars 

    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,...