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Collection of Extra Foils for CPS615 PDE Iterative Solution Discussion

This Introduces the three fundamental types of PDE's -- Elliptic, Parabolic and Hyperbolic and studies the numerical solution of Elliptic Equations

The sparse matrix formulation is used and iterative approaches -- Jacobi, Gauss Seidel and SOR are defined

These are motivated by analogies between equilibrium of diffusive equations and elliptic systems

Parallel Computing is Discussed for Gauss Seidel

Eigenvalue analysis is used to discuss convergence of methods

We discuss Multigrid methods at a simple level

Table of Contents for Collection of Extra Foils for CPS615 PDE Iterative Solution Discussion

001 CPS 615 -- Computational Science in Simulation Track Solution of 
    Simple Partial Differential Equations and  Iterative Solvers
002 Abstract of Simple Partial Differential Equations and Iterative 
    Solvers
003 Boundary Conditions I
004 Boundary Conditions II
005 Boundary Conditions III
006 Iterative Methods for Solving Sparse Matrices
007 Formalism for Iterative Methods
008 Preconditioning
009 Convergence of Jacobi in One Dimension
010 What is Easy/Hard for Jacobi?
011 Information Moves Slowly
012 Lowest Eigenvalue converges fastest
013 Successive Over Relaxation I
014 Successive Over Relaxation II
015 Some Mathematical Details
016 Multigrid Methods
017 Gauss Seidel is Slow I
018 Gauss Seidel is Slow II
019 Multigrid Philosophically
020 Multigrid Hierarchy
021 Basic Multigrid Ideas
022 Multigrid Algorithm: procedure MG(level, A, u, f)
023 Multigrid Cycles
024 What can we  do for  Parallel  Gauss Seidel?
025 16 by 16 Wavefront Parallel Gauss Seidel
026 Wavefront
027 Red Black Parallel Gauss Seidel I
028 Red  Black
029 Red Black Parallel Gauss Seidel II
030 Parallel Red Black
031 Red Black Parallel Gauss Seidel III
032 Red Black Parallel Gauss Seidel IV