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 Parallel Programming with MPI

    5.0 out of 5 stars 

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

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

  2. Introduction to TotalView

    0.0 out of 5 stars 

    Online Presentations | 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.

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

    5.0 out of 5 stars 

    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.

  4. Jupyter Notebooks for Scientific Programming

    0.0 out of 5 stars 

    Online Presentations | 06 Jan 2017 | Contributor(s):: Martin Hunt

    An overview of using Jupyter Notebooks for conveying scientific information.

  5. Katsu Kafe

    Groups

    Katsu Kafe is Katsujinken Foundations work-space for computational nanotechnology research, education, and collaboration. It is the prerequisite for employment on our High Performance Computing...

    https://nanohub.org/groups/katsujinkenfoundation

  6. Lecture 3: Integration Algorithms

    0.0 out of 5 stars 

    Presentation Materials | 05 Jan 2010 | Contributor(s):: Ashlie Martini

    Topics:General guidelinesVerlet algorithmPredictor-corrector methods

  7. Lecture 6: Neighbor Lists

    0.0 out of 5 stars 

    Presentation Materials | 05 Jan 2010 | Contributor(s):: Ashlie Martini

    Topics:Saving simulation timeVerlet listsCell lists

  8. Machine learned approximations to Density Functional Theory Hamiltonians - Towards High-Throughput Screening of Electronic Structure and Transport in Materials

    0.0 out of 5 stars 

    Online Presentations | 13 Dec 2016 | Contributor(s):: Ganesh Krishna Hegde

    We present results from our recent work on direct machine learning of DFT Hamiltonians. We show that approximating DFT Hamiltonians accurately by direct learning is feasible and compare them to existing semi-empirical approaches to the problem. The technique we have proposed requires little...

  9. Machine Learning with MATLAB

    0.0 out of 5 stars 

    Online Presentations | 11 Mar 2022 | Contributor(s):: Gaby Arellano Bello

    In this session, we explore the fundamentals of machine learning using MATLAB. We introduce machine learning techniques available in MATLAB to quickly explore your data, evaluate machine learning algorithms, compare the results and apply the best technique to your problem.

  10. MATLAB Scripts for "Quantum Transport: Atom to Transistor"

    4.0 out of 5 stars 

    Downloads | 15 Mar 2005 | Contributor(s):: Supriyo Datta

    Tinker with quantum transport models! Download the MATLAB scripts used to demonstrate the physics described in Supriyo Datta's book Quantum Transport: Atom to Transistor. These simple models are less than a page of code, and yet they reproduce much of the fundamental physics observed in...

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

    0.0 out of 5 stars 

    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,...

  12. MCW07 Simple Models for Molecular Transport Junctions

    0.0 out of 5 stars 

    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.

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

    0.0 out of 5 stars 

    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.

  14. Memory-Efficient Particle Annihilation Algorithm for Wigner Monte Carlo Simulations

    0.0 out of 5 stars 

    Online Presentations | 10 Feb 2016 | Contributor(s):: Paul Ellinghaus

    IWCE 2015 presentation. The Wigner Monte Carlo solver, using the signed-particle method, is based on the generation and annihilation of numerical particles. The memory demands of the annihilation algorithm can become exorbitant, if a high spatial resolution is used, because the entire discretized...

  15. Modeling and Analysis of VLSI Interconnects

    0.0 out of 5 stars 

    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...

  16. Modeling and Simulation of Sub-Micron Thermal Transport

    0.0 out of 5 stars 

    Online Presentations | 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 Fourier's...

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

    0.0 out of 5 stars 

    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...

  18. 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...

  19. MOSCNT: code for carbon nanotube transistor simulation

    3.5 out of 5 stars 

    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...

  20. Myron DSilva

    https://nanohub.org/members/182103