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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.

Online Presentations (1-20 of 77)

  1. ECE 595E Lecture 36: MEEP Tutorial II

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    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

    https://nanohub.org/resources/17558

  2. ECE 595E Lecture 35: MEEP Tutorial I

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

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

    https://nanohub.org/resources/17557

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

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    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 diverse …

    https://nanohub.org/resources/17535

  4. [Illinois] An Overview of Multiscale Simulation Algorithms: Guidelines and Pitfalls to Avoid

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    29 Dec 2012 | Online Presentations | Contributor(s): Richard Braatz

    …

    https://nanohub.org/resources/16159

  5. The Pioneers of Quantum Computing

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    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 that …

    https://nanohub.org/resources/8067

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

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    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 expressions Tight …

    https://nanohub.org/resources/8599

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

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    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 questions …

    https://nanohub.org/resources/8598

  8. Nanoelectronic Modeling Lecture 26: NEMO1D -

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    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 …

    https://nanohub.org/resources/8596

  9. Nanoelectronic Modeling Lecture 27: NEMO1D -

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    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 requirements …

    https://nanohub.org/resources/8597

  10. Nanoelectronic Modeling Lecture 21: Recursive Green Function Algorithm

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    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 …

    https://nanohub.org/resources/8388

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

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    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 …

    https://nanohub.org/resources/7442

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

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    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 …

    https://nanohub.org/resources/7376

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

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    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 …

    https://nanohub.org/resources/7372

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

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    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 …

    https://nanohub.org/resources/6856

  15. Quantitative, Kinetic Models of Cellular Circuits

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    04 Apr 2009 | Online Presentations | Contributor(s): Michael R. Brent

    Living cells contain complex, analog circuits that regulate the rate at which each gene produces its product. The kinetic properties of these circuits enable cells to respond to changes in their …

    https://nanohub.org/resources/6374

  16. The Multicore Era: Crisis or (and?) Opportunity?

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    27 Mar 2009 | Online Presentations | Contributor(s): Mithuna Thottethodi

    This talk will provide a brief overview of how we got to the multicore era, the implications and challenges for hardware/software developers and users, and some informed speculation on where the …

    https://nanohub.org/resources/6523

  17. Experiences with nonintrusive polynomial Chaos and stochastic collocation methods for uncertainty analysis and design

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    13 Mar 2009 | Online Presentations | Contributor(s): Michael S. Eldred

    Non—intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification due to their abilities to produce functional …

    https://nanohub.org/resources/5910

  18. Nanoparticle and Colloidal Simulations with Molecular Dynamics

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    05 Dec 2008 | Online Presentations | Contributor(s): Steve Plimpton

    Modeling nanoparticle or colloidal systems in a molecular dynamics (MD) code requires coarse-graining on several levels to achieve meaningful simulation times for study of rheological and other …

    https://nanohub.org/resources/5668

  19. OpenMP Tutorial

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    25 Nov 2008 | Online Presentations | Contributor(s): Seung-Jai Min

    This tutorial consists of three parts. First, we will discuss about how OpenMP is typically used and explain OpenMP programming model. Second, we will describe important OpenMP constructs and data …

    https://nanohub.org/resources/5874

  20. Introduction to Parallel Programming with MPI

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    24 Nov 2008 | Online Presentations | 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 …

    https://nanohub.org/resources/5932

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