Next:
Finite and Infinite
Finite and Infinite Dimensional Matrices as Operators
as an Operator and Its Scalar Products
as a Hermitean Operator
The Laplacian as a (Matrix) Operator
Mapping of Function Spaces to a Finite Number of Dimensions
Mathematical and Pseudo Code Form of Gauss Seidel Iteration Method
Mathematical (Matrix) Form of Gauss Seidel
Parallelism in Gauss-Seidel Iteration
Matrix Example Stencil
Matrix---Wavefront Parallelism for Gauss Seidel
The Red-Black Two Phase Parallel Gauss Seidel Iteration
Analysis of Parallel Red Black Gauss Seidel
Eigenvalues of Gauss Seidel Iteration Matrix
Comparison of Convergence of Gauss-Seidel and Jacobi Iteration
Successive Overrelaxation Iteration Method (SOR)
Convergence of SOR Compared to Jacobi and Gauss Seidel
Estimate of Over Relaxation Parameter
Pseudo Code for SOR---Successive Over Relaxation
Integral Formulation of Finite Element Method
Variation in Integral
Equivalence of Integral and Differential Formulation of Laplace's Equation
Discretization of Integral
Triangular Elements in Two Dimensions
Example for Two-Dimensional Triangular Elements
Bilinear Form of Integral with Triangular Elements
Formula for Stiffness Matrix Element
Finite Element Equations
Structure of Stiffness Matrix and Its Assembly
Conditions on Triangulation
Introduction to Poor Person's Conjugate Gradient
Conjugate Gradient Iteration for Quadratic Form
Conjugate Gradient and Method of Steepest Descent
Conjugate Gradient for Finite Element Problems
Poor Person's Conjugate Gradient and Eigenvalues of Matrix
Diagonalization of Quadratic Form
Diagonalization of Conjugate Gradient Equations
Convergence of Conjugate Gradient in Diagonalized Form
Clarification of Eigenvalue Analysis for Conjugate Gradient and Jacobi Iteration
Intuitive Description of Poor Person's Conjugate Gradient Algorithm
Improvement of Poor Person's Conjugate Gradient with Orthonormal Iteration
Full Conjugate Gradient Algorithm
Overview of Parallelism in Conjugate Gradient
Parallel Issues in Calculation of Matrix Elements
Scalar Products in Parallel Conjugate Gradient
Preconditioning in Conjugate Gradient
Convergence of Conjugate Gradient
Geoffrey Fox,
Northeast Parallel Architectures Center
at Syracuse University, gcf@npac.syr.edu
