Algorithms

Algebra

Designing fast linear algebra kernels in the presence of memory hierarchies is a set of lectures given by Jim Demmel at Berkeley as part of his course Applications of Parallel Computers. The emphasis of these lectures is on the study of memory hierarchies by asking how fast one can perform certain simple linear algebra "kernel" routines, like matrix multiply. More complicated algorithms are built from these kernels, as was described there, so understanding the kernels is essential to understanding the more complicated routines.

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Numerical Recipes homepage at Harvard containing downloadable software and other relevant info to those books.

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Monte Carlo Techniques

Statistics and Random Numbers from the course Introduction to Computational Science at Syracuse.

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Background material on Random Number Generators, from the CSEP book at Oak Ridge National Lab.

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Monte Carlo Techniques is a tutorial page on the subject as part of a computational physics course taught by Rubin Landau at Oregon State.

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Monte Carlo Methods is a lecture by Eric Ormand at Tennessee and Oak Ridge National Laboratory as part of a computational science course given by Guidry and Strayer at Tennessee and Oak Ridge.

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Numerical Integration

Numerical Integration Newton-Cotes formulae and Monte Carlo techniques, from the course Introduction to Computational Science at Syracuse.

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Numerical Linear Algebra / Matrix Operations

Numerical Linear Algebra is a book by Trefethen and Bau (SIAM, April 1997) at Cornell. A number of chapters of this book are online. Also, here is a short essay on numerial analysis by Trefethen.

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A good introduction to numerical linear algebra comes from the HPSC group at the University of Colorado at Boulder as a Review of Selected Topics from Numerical Analysis covering basic matrix analysis, elementary Ordinary Differential equations and Fourier Analysis.

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Numerical Linear Algebra for Parallel Machines a chapter from the CSEP book at Oak Ridge National Lab.

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Eigenvalues and Eigenvectors, from the course Introduction to Computational Science at Syracuse.

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The book Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, by Demmel, Dongarra, et al. available at Netlib is a survey of templates, iterative methods, preconditioners and parallel computing issues in solving linear algrebraic systems of equations.

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Slides from a 90 minute tutorial on templates by J. Dongarra (1995), available at Netlib.

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LAPACK User's Guide - Release 2.0, is a documentation manual for the LAPACK version 2.0 library of Fortran 77 subroutines for numerical linear algebra. Available at Netlib.

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Mathematical Programming in Machine Learning, is the mathematical programming section within the Computer Science Department at the University of Wisconsin - Madison. Course materials on optimization are available.

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CS237A Numerical Linear Algebra and CS339 Parallel Numerical Analysis, are given by the Scientific Computing and Computational Mathematics Program at Stanford University.

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Parallel Numerical Libraries, at the Edinburgh Parallel Computing Center Training and Education Center.

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Parallel Numerical Algorithms is a course given by Michael Heath at University of Illinois at Urbana-Champaign. It covers among other methods, iterative methods for linear systems.

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Nonlinear Problems

Unstructured Grid (UG) homepage at Univ. of Stuttgart, Germany. UG is a flexible software tool for the numerical solution of partial differential equations on unstructured meshes in two and three space dimensions using multigrid methods. Few applications of this software are structural mechanics, multiphase flow in porous media, parallel applications, Navier-Stokes, etc.

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Numerical ODE solvers - Particle systems

ODE's and Computing Techniques for Particle Systems and the same material, from the course Introduction to Computational Science at Syracuse.

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Background material on numerical methods for ODE's, from the CSEP book at ORNL.

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HPSC, High Performance Scientific Computing, introduction to molecular dynamics from the University of Colorado at Boulder. The file is located in "Retrieving the Materials" section of the page.

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Solving Field Equations / PDE's

Finite Differences

Iterative Methods for Partial Differential Equations from the course Introduction to Computational Science at Syarcuse.

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Motivation for Partial Differential Equations This has extensive discussion of CFD and the Navier Stokes equation. It also has initial remarks on relative role of PDE's, Monte Carlo, and particle dynamics. From Introduction to Computational Science course at Syracuse.

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Basic Discussion of PDE's, in the CSEP Project book, with examples on Some HPC Issues in PDE's also from theCSEP book at ORNL.

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A very good discussion of iterative methods is in Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods by Dongarra et al. available at Netlib.

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Educational Materials from the Retooling Project, field simulations at Syracuse.

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Finite Elements

Finite Element Methods and Conjugate Gradient Solvers, with analogies to minimization methods. From the Introduction Computational Science course at Syracuse.

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Also check Jonathan Shewchuk's review paper at CMU on the Conjugate Method entitled An Introduction to the Conjugate Method Without the Agonizing Pain, in the "Reports" section of the page.

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Finite Element Mesh Generation on mesh as well as grid generation in Aachen, Germany.

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Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations is a textbook written during 1985-1994 by Lloyd N. Trefethen of Cornell University and used in graduate courses at MIT and Cornell on the numerical solution of partial differential equations.

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Multigrid Techniques

A good starting point to multigrid techniques is an answer to this question: What are Multigrid Methods? at Yale University. Also, here is a short document (in Adobe PDF) entitled Mutligrid and Multilevel Methods in Science and Engineering.

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A general multigrid algorithm is given here: The Multigrid Workbench: Algorithm. It is a linear iteration of this form: The Multigrid Workbench: Linear Iterations. Also multigrid can be applied in different cycling strategies as shown here. Available from the Computer Science Department at Yale University.

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A multigrid algorithm uses the following algorithmic components.
- Smoother located at Yale.
- Residual computation located at Yale.
- Restriction located at Yale.
- Coarse Grid solver located at Yale.
- Interpolation located at Yale.
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MGNet page at Yale contains a list of multigrid software packages.

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Domain decomposition is an area closely related to multigrid methods. Here is a page containing Various Domain Decomposition Links at DDM.

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Optimization

The Network-Enabled Optimization System (NEOS) from the Optimization Technology Center at Argonne National Lab includes a set of case studies as well as descriptions of available software.

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Constrained and Unconstrained Optimization is part of the Stony Brook Algorithm Repository at SUNY, Stony Brook.

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A list of software packages and other related links for global optimization at University of Vienna, Austria is available here, at Boston University.

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A useful link at Arizona State University containing various global and local optimization methods and software is the Decision Tree for Optimization Software.

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An interesting optimization page in Osnabrueck, Germany is about complexity results of scheduling problems.

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Mathematical Programming in Machine Learning, is the mathematical programming section within the Computer Science Department at the University of Wisconsin - Madison. Course materials on optimization are available.

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Simulation Modeling

Computational Physics, an undergraduate physics course at the University of Western Australia focusing on simulation, modelling and visualization.

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Scientific Visualization

Computational Physics, an undergraduate physics course at the University of Western Australia focusing on simulation, modelling and visualization.

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Application Visualisation System (AVS), and Visualisation in an HPC Environment at Manchester and North Training and Education Center.

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Scientific Visualization, at the Edinburgh Parallel Computing Center Training and Education Center.

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Shastra is a research lab at Purdue University doing work in geometric modeling, simulation, interrogative visualization and design prototyping environments.

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Scientific Computing and Visualization at Boston University lists tutorials and other materials on scientific computing and visualization.

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Scientific Visualization at the Pittsburgh Supercomputing Center.

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A list of Scientific Visualization Sites is at the NASA Ames Research Center. It lists academic centers, government labs, military centers as well as companies conducting research in this area.

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Visualization at the Cornell Theory Center containing pictures, movies, educational materials, software, and much descriptive text. They make extensive use of the IBM Data Explorer visualization system and WaveFront's Advanced Visualizer.

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Visualization Codes at MIT's Department of Aeronautics and Astronautics containing visualization systems for unsteady, unstructured (and structured) CFD visualization (mostly).

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MetaComputing

MetaComputing an overview of technologies and issues for metacomputing by Mark Baker and Geoffrey Fox at Syracuse.

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Nimrod: A Tool for High Performance Distributed Metacomputing developed by David Abramson at Monash University in Australia to address issues such as metacomputing, metacomputing and parametrized simulation, etc.

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The abovementioned Nimrod project indirectly influnced the development of a new set of metacomputing tools named Clustor by Active Tools Inc. of San Francisco.

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Northeast Parallel Architectures Center (NPAC) at Syracuse University. The content of these pages may be used freely for educational purposes. Some of the material is under individual copyright. Send comments to Saleh Elmohamed, saleh@npac.syr.edu. Last updated 5/24//97.