Algorithms and Applications

• 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.
• On mesh and grid generation take a look at Finite Element Mesh Generation.
• For a good survey on N-Body Methods Resources, see this page at EPCC.