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.

Online Presentations (1-20 of 84)

  1. ECE 695NS Lecture 3: Practical Assessment of Code Performance

    25 Jan 2017 | Online Presentations | Contributor(s): Peter Bermel

    Outline: Time Scaling Examples General performance strategies Computer architectures Measuring code speed Reduce strength Minimize array writes Profiling

    http://nanohub.org/resources/25677

  2. ECE 695NS Lecture 2: Computability and NP-hardness

    13 Jan 2017 | Online Presentations | Contributor(s): Peter Bermel

    Outline: Overview Definitions Computing Machines Church-Turing Thesis Polynomial Time (Class P) Class NP Non-deterministic Turing machines Reducibility Cook-Levin...

    http://nanohub.org/resources/25676

  3. Jupyter Notebooks for Scientific Programming

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

    An overview of using Jupyter Notebooks for conveying scientific information.

    http://nanohub.org/resources/25550

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

    13 Dec 2016 | Online Presentations | 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...

    http://nanohub.org/resources/25379

  5. High Accuracy Atomic Force Microscope with Self-Optimizing Scan Control

    19 Sep 2016 | Online Presentations | Contributor(s): Ryan (Young-kook) Yoo

    Atomic force microscope (AFM) is a very useful instrument in characterizing nanoscale features, However, the original AFM design, based on piezo-tube scanner, had slow response and non-orthogonal...

    http://nanohub.org/resources/24927

  6. Data-Centric Models for Multilevel Algorithms

    07 Feb 2016 | Online Presentations | Contributor(s): Samuel Guiterrez

    Today, computational scientists must contend with a diverse set of supercomputer architectures that are capable of exposing unprecedented levels of parallelism and complexity. Effectively placing,...

    http://nanohub.org/resources/23532

  7. Range Decomposition: A Low Communication Algorithm for Solving PDEs on Massively Parallel Machines

    07 Feb 2016 | Online Presentations | Contributor(s): Tom Manteuffel

    The Range Decomposition (RD) algorithm uses nested iteration and adaptive mesh refinement locally before performing a global communication step. Only several such steps are observed to be...

    http://nanohub.org/resources/23540

  8. A Scalable Algorithm for Inverse Medium Problems with Multiple Sources

    04 Feb 2016 | Online Presentations | Contributor(s): Keith Kelly

    We consider the problem of acoustic scattering as described by the free-space, time-harmonic scalar wave equation given by   (0.1)   along with radiation boundary conditions. Here, is a...

    http://nanohub.org/resources/23498

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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