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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 (1-20 of 184)

  1. Hao Zhuang

    http://nanohub.org/members/105541

  2. ECE 595E Lecture 36: MEEP Tutorial II

    30 Apr 2013 | Online Presentations | Contributor(s): Peter Bermel

    Outline: Recap from Monday Examples Multimode ring resonators Isolating individual resonances Kerr nonlinearities Quantifying third-harmonic generation

    http://nanohub.org/resources/17558

  3. Integrated Imaging Seminar Series

    30 Apr 2013 | Series | Contributor(s): Charles Addison Bouman

    Integrated imaging seminar series is jointly sponsored by the Birck Nanotechnology Center and ECE. Integrated Imaging is defined as a cross-disciplinary field combining sensor science, information...

    http://nanohub.org/resources/17591

  4. ECE 595E Lecture 35: MEEP Tutorial I

    18 Apr 2013 | Online Presentations | Contributor(s): Peter Bermel

    Outline: MEEP Interfaces MEEP Classes Tutorial examples: Waveguide Bent waveguide

    http://nanohub.org/resources/17557

  5. Data-adaptive Filtering and the State of the Art in Image Processing

    15 Apr 2013 | Online Presentations | Contributor(s): Peyman Milanfar

    In this talk, I will present a practical and unified framework for understanding some common underpinnings of these methods. This leads to new insights and a broad understanding of how these...

    http://nanohub.org/resources/17535

  6. ECE 595 Course Policy - Spring 2013

    03 Jan 2013 | Teaching Materials | Contributor(s): Peter Bermel

    A description of the key policies that will govern the administration of ECE 595 on "Numerical Methods" in Spring 2013.

    http://nanohub.org/resources/16189

  7. Hamed Abdy

    http://nanohub.org/members/50166

  8. The Pioneers of Quantum Computing

    19 Nov 2010 | Online Presentations | Contributor(s): David P. Di Vincenzo

    This talk profiles the persons whose insights and visions created the subject of quantum information science. Some famous, some not, they all thought deeply about the puzzles and contradictions...

    http://nanohub.org/resources/8067

  9. Nanoelectronic Modeling Lecture 29: Introduction to the NEMO3D Tool

    04 Aug 2010 | Online Presentations | Contributor(s): Gerhard Klimeck

    This presentation provides a very high level software overview of NEMO3D. The items discussed are: Modeling Agenda and Motivation Tight-Binding Motivation and basic formula...

    http://nanohub.org/resources/8599

  10. Nanoelectronic Modeling Lecture 28: Introduction to Quantum Dots and Modeling Needs/Requirements

    20 Jul 2010 | Online Presentations | Contributor(s): Gerhard Klimeck

    This presentation provides a very high level software overview of NEMO1D. Learning Objectives: This lecture provides a very high level overview of quantum dots. The main issues and...

    http://nanohub.org/resources/8598

  11. Nanoelectronic Modeling Lecture 26: NEMO1D -

    09 Mar 2010 | Online Presentations | Contributor(s): Gerhard Klimeck

    NEMO1D demonstrated the first industrial strength implementation of NEGF into a simulator that quantitatively simulated resonant tunneling diodes. The development of efficient algorithms that...

    http://nanohub.org/resources/8596

  12. Nanoelectronic Modeling Lecture 27: NEMO1D -

    09 Mar 2010 | Online Presentations | Contributor(s): Gerhard Klimeck

    This presentation provides a very high level software overview of NEMO1D. The items discussed are: User requirements Graphical user interface Software structure Program developer...

    http://nanohub.org/resources/8597

  13. Nanoelectronic Modeling Lecture 21: Recursive Green Function Algorithm

    07 Feb 2010 | Online Presentations | Contributor(s): Gerhard Klimeck

    The Recursive Green Function (RGF) algorithms is the primary workhorse for the numerical solution of NEGF equations in quasi-1D systems. It is particularly efficient in cases where the device is...

    http://nanohub.org/resources/8388

  14. Lecture 6: Neighbor Lists

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

    Topics: Saving simulation time Verlet lists Cell lists

    http://nanohub.org/resources/8121

  15. Lecture 3: Integration Algorithms

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

    Topics: General guidelines Verlet algorithm Predictor-corrector methods

    http://nanohub.org/resources/8118

  16. Short Course on Molecular Dynamics Simulation

    13 Oct 2009 | Courses | Contributor(s): Ashlie Martini

    This set of ten presentations accompanied a graduate level course on Molecular Dynamics simulation. The specific objective of the course (and the presentations) is to provide: 1. Awareness of...

    http://nanohub.org/resources/7570

  17. Illinois ECE 498AL: Programming Massively Parallel Processors, Lecture 15: Kernel and Algorithm Patterns for CUDA

    30 Sep 2009 | Online Presentations | Contributor(s): Wen-Mei W Hwu

    Kernel and Algorithm Patterns for CUDA Topics: Reductions and Memory Patterns Reduction Patterns in CUDA Mapping Data into CUDA's Memories Input/Output Convolution Generic Algorithm...

    http://nanohub.org/resources/7442

  18. Illinois ECE 498AL: Programming Massively Parallel Processors, Lecture 13: Reductions and their Implementation

    15 Sep 2009 | Online Presentations | Contributor(s): Wen-Mei W Hwu

    Structuring Parallel Algorithms Topics: Parallel Reductions Parallel Prefix Sum Relevance of Scan Application of Scan Scan on the CPU First attempt Parallel Scan Algorithm Work...

    http://nanohub.org/resources/7376

  19. Illinois ECE 498AL: Programming Massively Parallel Processors, Lecture 12: Structuring Parallel Algorithms

    15 Sep 2009 | Online Presentations | Contributor(s): Wen-Mei W Hwu

    Structuring Parallel Algorithms Topics: Key Parallel Programming Steps Algorithms Choosing Algorithm Structure Mapping a Divide and Conquer algorithm Tiled Algorithms Increased work...

    http://nanohub.org/resources/7372

  20. Experiment vs. Modelling: What's the problem?

    10 Aug 2009 | Online Presentations | Contributor(s): William L. Barnes

    Progress in plasmonics has been greatly assisted by developments in experimental techniques and in numerical modelling. This talk will look at some of the difficulties that emerge when...

    http://nanohub.org/resources/6856

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