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.

Resources (41-60 of 135)

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

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

  2. First Principles-based Atomistic and Mesoscale Modeling of Materials

    01 Dec 2005 | | Contributor(s):: Alejandro Strachan

    This tutorial will describe some of the most powerful and widely used techniques for materials modeling including i) first principles quantum mechanics (QM), ii) large-scale molecular dynamics (MD) simulations and iii) mesoscale modeling, together with the strategies to bridge between them. These...

  3. First Principles-Based Modeling of materials: Towards Computational Materials Design

    20 Apr 2006 | | Contributor(s):: Alejandro Strachan

    Molecular dynamics (MD) simulations with accurate, first principles-based interatomic potentials is a powerful tool to uncover and characterize the molecular-level mechanisms that govern the chemical, mechanical and optical properties of materials. Such fundamental understanding is critical to...

  4. Geometric Multigrid for MHD Simulations with Nedelec Finite Elements on Tetrahedral Grids

    02 Feb 2016 | | Contributor(s):: Chris Hansen

    The Magneto-HydroDynamic (MHD) model is used extensively to simulate macroscopic plasma dynamics in Magnetic Confinement Fusion (MCF) devices. In these simulations, the span of time scales from fast wave dynamics to the desired evolution of equilibrium due to transport processes is large,...

  5. Hierarchical Physical Models for Analysis of Electrostatic Nanoelectromechanical Systems (NEMS)

    05 Jan 2006 | | Contributor(s):: Narayan Aluru

    This talk will introduce hierarchical physical models and efficient computational techniques for coupled analysis of electrical, mechanical and van der Waals energy domains encountered in Nanoelectromechanical Systems (NEMS). Numerical results will be presented for several silicon...

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

    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...

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

    19 Sep 2016 | | 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 behavior, inadequate to address the metrology needs of industrial applications: accuracy,...

  8. HPC and Visualization for multimillion atom simulations

    21 Jun 2005 | | Contributor(s):: Gerhard Klimeck

    This presentation gives an overview of the HPC and visulaization efforts involving multi-million atom simulations for the June 2005 NSF site visit to the Network for Computational Nanotechnology.

  9. HPCW Introduction to Parallel Programming with MPI

    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,...

  10. HPCW Parallel Programming Models

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

  11. HPGMG: Benchmarking Computers Using Multigrid

    04 Feb 2016 | | Contributor(s):: Jed Brown

    HPGMG (https://hpgmg.org) is a geometric multigrid benchmark designed to measure the performance and versatility of computers. For a benchmark to be representative of applications, good performance on the benchmark should be sufficient to ensure good performance on most important applications and...

  12. Human-Interpretable Concept Learning via Information Lattices

    23 May 2019 | | Contributor(s):: Lav R. Varshney

    The basic idea is an iterative discovery algorithm that has a student-teacher architecture and that operates on a generalization of Shannon’s information lattice, which itself encodes a hierarchy of abstractions and is algorithmically constructed from group-theoretic foundations.

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

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

    Structuring Parallel AlgorithmsTopics: Key Parallel Programming Steps Algorithms Choosing Algorithm Structure Mapping a Divide and Conquer algorithm Tiled Algorithms Increased work per thread Double Buffering Loop Fusion and Memory Privatization Pipeline or "Spatial Computing Model" These lecture...

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

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

    Structuring Parallel AlgorithmsTopics: Parallel Reductions Parallel Prefix Sum Relevance of Scan Application of Scan Scan on the CPU First attempt Parallel Scan Algorithm Work efficiency considerations Improving Efficiency Use Padding to reduce conflicts Global Synchronization in CUDAThese...

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

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

    Kernel and Algorithm Patterns for CUDATopics: Reductions and Memory Patterns Reduction Patterns in CUDA Mapping Data into CUDA's Memories Input/Output Convolution Generic Algorithm Description What could each thread be assigned? Thread Assignment Trade-offs What memory Space does the Data use?...

  16. Integrated Imaging Seminar Series

    30 Apr 2013 | | 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 processing, and computer systems for the creation of novel imaging and sensing systems. In this...

  17. Interactive Learning Tools for Scientific Computing and Data Analysis Using R

    29 Jul 2020 | | Contributor(s):: Cindy Nguyen, Rei Sanchez-Arias

    Root-finding methods and numerical optimization techniques with applications in science, engineering, and data analysis

  18. Introduction to Parallel Programming with MPI

    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...

  19. Introduction to TotalView

    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.

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

    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.