Applications and Algorithms

Table of Contents

Algorithms

1. Course Materials

   • Lecture slides: Statistics and Random Numbers, in preparation for Monte Carlo Integrals.
   • Background materials on Random Number Generators (RNG), from the CSEP book.
   • Lecture slides: ODE's and Computing Techniques for Particle Systems, and the same material appeared in written text.
   • Background materials on Ordinary Differential Equations, from the CSEP book.
   • Numerical Integration Module including details on Monte Carlo Methods.
   • Lecture slides:Adaptive Parallel Computing Techniques for Numerical Integration apply parallel computing to numerical integration.
   • Lecture slides: Iterative Methods for Partial Differential Equations.
   • Lecture slides:Motivation for Partial Differential Equations where this has extensive discussion of CFD and the Navier Stokes equation which was prepared for CPS713 and can be ignored here. The initial remarks on relative role of PDE's, Monte Carlo, and particle dynamics has value.
   • Further references are: Basic Discussion of PDE's in CSEP Project.
   • More examples in Material Balance Section.
   • 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.
   • A good introduction to numerical linear algebra comes from the HPSC group at the University of Colorado covering basic matrix analysis, elementary ODE's and Fourier Analysis.
   • The full HPSC material is available in postscript by ftp. You may need to fetch the numerical analysis module for use in the course.
   • Lecture slides: Linear Algebra Presentation that continues from the HPSC resource with eigenvalues and eigenvectors.
   • Lecture slides:Finite Element and Conjugate Gradient Presentation with analogies to minimization methods.
   • Lecture slides:Parallel Full Matrix Algorithms.
   • More parallel computing materials, algorithms, tutorials are available at Computational Science page.

2. General Resources

   • Parallel Computing Works! is an online book by G. C Fox, R. D. Williams, and P. C. Messina. A highly recommended book to read.
   • Designing and Building Parallel Programs by Ian Foster is an online book, a collection of public domain parallel software tools, a collection of Web Tours providing access to other information on Parallel Computing, and various educational resources.
   • Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods is an online book by Demmel, Dongarra, et al. It focuses on templates for iterative methods such as Conjugate Gradient (CG) and Successive Overrelaxation (SOR).
   • Lecture notes by Jim Demmel on Design and Implementation of LAPACK and ScaLAPACK. (UCB)
   • Lecture notes by Jime Demmel on Solving the Discrete Poisson Equation using Jacobi, SOR, Conjugate Gradients, and the FFT. (UCB)
   • Supercomputing and Parallel Computing Resources is a collection of pointers to various pages containing software resources. (CMU)
   • Computational Science Resources is a collection of online resources in computational methods, application areas, roadmaps, courses, hardware, and software. (OR)
   • Parallel Computing is a one day course given by Minty, Davey, and Simpson of EPCC. There are also other related tools. (UK)
   • On mesh and grid generation take a look at Finite Element Mesh Generation. (DE)
   • For a good survey on N-Body Methods Resources, see this page at EPCC. (UK)
   • Global Educational Resources for HPC is quite a comprehensive collection of resources in parallel computing education, courses and tutorials, books online, bibliographies, software online, and parallel research groups. (RIT)
   • Programming Tools--Languages and Libraries is a set of parallel software tools and libraries. Tools such as Scalable Unstructured Mesh Computation and libraries such as Chameleon, etc. (ANL)
   • NAS Parallel Tools Group Hotlist of useful tools in design/analysis , programming models and paradigms, process control, debugging and performance analysis/visualization, etc. (NASA)

Computational Methods

1. Course Materials

   • Optimization Methods is a list of lecture slides covering most of the pratical optimization methods for the computational science simulation track. Also, the set includes a list of suggested projects in the area. (GCF at NPAC)
   • A set of lecture slides covering Various Computational Methods in the HPCC field. Example methods shown are from areas such as Earth Science, Biology, Chemistry, and Fluid Dynamics. (GCF at NPAC)
   • Comparison of Computational Complexity between Direct and Iterative Methods. (GCF at NPAC)
   • Comparison of Different Methods for Solving Linear Convection Equation. (GCF at NPAC)
   • Computational methodologies suggested by complex systems. (GCF at NPAC)
   • Multiscale Methods in parallel data decomposition. (GCF at NPAC)
   • Comparison of Physical Optimization Methods. (GCF at NPAC)

2. General Resources

   • Monte Carlo Methods (by Guidry et al.) for integration are rooted in the concept that a part of the function to be integrated over may be thought of as a normalized probability distribution over the region of integration. (UK)
   • Lecture notes by Demmel on Solving the Discrete Poisson Equation using the Multigrid method. (UCB)
   • Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods is an online book by Demmel, Dongarra, et al. It focuses on templates for iterative methods such as Conjugate Gradient (CG) and Successive Overrelaxation (SOR). (UCB)
   • Introduction to Monte Carlo Methods from the CSEP book. (ORNL)

Applications Areas

1. Course Materials

   • None is available.

2. General Resources

   • Computational Fluid Dynamics for Astrophysics is a lecture was given by Univ. of Tennessee and Oak Ridge as part of the Computational Science Education Project.
   • Earth Sciences Resources is essentially a collection of resources, etc. dealing with studies in Earch Science.
   • Atmospheric Sciences Resources. Web resources maintained by the US Geological Survey.
   • Biology Resources is a collection of pointers to resources in biology. Maintained by the US Geological Survey.
   • Molecular Modeling maintained by the Center for Molecular Modeling of the National Institute of Health. It points to software and hardware resources in the field of Molecular Modeling.
   • Computational Molecular Biology is a collection of resources and documents in Sequence Analysis, Molecular Biology Software, and other related resources. This page is maintained by the molecular biology section of NIH.
   • Physics Resources is a link to Mike Guidry's collection of physics resources. This is part of the Computational Science Education Projects.
   • Guide to Available Mathematical Software. NIST provides a comprehensive guide to wide range of available mathematical software listed by package name and module name with short abstracts of the module.
   • UCB/NASA Earth Observing System, Distributed Information System as part of NASA's EOS."End-to-End Problems in EOSDIS" is a NASA-sponsored multi-year project investigating alternative data management strategies for NASA's Earth Observing System (EOS).
   • Atmospheric Chemistry Model is a NASA-sponsored model to develop a state-of-the-art Earth System Model (ESM) that will be comprised of a coupled atmosphere and ocean system including chemical tracers that are found in, and may be exchanged between, the atmosphere and the oceans.
   • Real-World Solutions With Cray Research Systems is a sampling of case histories revealing the real-world impact of Cray systems in solving some challenging problems!
   • Here is a very interesting page containing a set of Parallel Algorithm Animation for various parallel algorithms.

General References and Roadmaps

1. Course Materials

   • None is available.

2. General Resources

   • The NHSE HPCC Roadmap is a guide to High Performance Computing and Communications (HPCC) applications, algorithms, software and enabling technologies. It is developed as part of the National HPCC Software Exchange.
   • Sequence analysis tools for Protein identification, DNA -> Protein, similarity searches, pattern and profile searches , primary structure analysis, secondary structure prediction, transmembrane regions detection, etc.
   • Applications of Computational Geometry is a collection of various areas in which ideas from discrete and computational geometry (meaning mainly low-dimensional Euclidean geometry) meet some real world applications.
   • The topic of computational gene recognition has become more and more important as long DNA being sequenced in the Human Genome Project. Here is a bibliography in Computational Gene Recognition.
   • Supercomputing and Parallel Computing Resources of conferences, research groups, vendors, and supercomputers.
   • Lectures in Various Computational Science Methods for the physical and life sciences presented at ORNL by Guidry and Strayer.
   • Presentations in Hypertext Format by Guidry et al. at ORNL as part of the CSEP.
   • Introduction to Monte Carlo Methods from the CSEP book.