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| 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 approachs -- Jacobi, Gauss Seidel and SOR are defined |
| These are motivated by analogies between equilibrium of diffusive equations and elliptic systems |
| Eigenvalue analysis is used to discuss convergence of methods |
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Iterative Solver Module
Abstract of PDE and Iterative Solver CPS615 Module
Partial Differential Equations: Use in Continuum Physics
Examples of Different Types of Partial Differential Equations:
Examples of Different Types of Partial Differential Equations:
Examples of Different Types of PDE's: Laplace and Poisson Elliptic Equations
What Conditions are sufficient for solution of PDE's -- Cauchy Boundary Conditions and Hyperbolic,Parabolic and Elliptic PDE's
Closed Boundaries; Dirichlet and Neumann Conditions
Examples of Open(Diffusion) and Closed(Laplace) Boundary Conditions
Solutions to Elliptic Equations by Finite Differences
Central Difference Operator with error O(h2)
Difference Equation form of the Operator to solve Laplace's equation
The 12 by 12 Block Tridiagonal Equations Coming from Laplace's Equation on a Tiny 5 by 6 Grid
General Form of Sparse Matrix Coming from Laplace's Equation - I
General Form of Sparse Matrix Coming from Laplace's Equation in two dimensions - II
Iterative Methods and Analogy to Diffusion with an Artificial Time
Solution of Artificial Time Equation as a Diffusion System Discretized in Space and Time
General 2D Artificial Time Diffusion Equation in Iterative Form
Traditional Iterative Methods as Special Cases of Artificial Time Diffusion Formalism
Simple Iterative Methods: Jacobi, Gauss-Seidel, SOR
Matrix Notation for Iterative Methods
General Iteration Matrix Splitting and Preconditioning
Explicit Form of General Jacobi Iteration
The Special Case of Jacobi Iteration for Laplace's Equation
Pseudo Code for the Jacobi Method
Formalism for Convergence of Stationary Iterative Methods
Eigenvalue Analysis of Iterative Methods
Estimation of largest Eigenvalue in One Dimension
Eigenvalues and Convergence Rate of Jacobi Iteration
Difficult and Easy Eigenfunctions Controlling
Decoupling of Even and Odd Grid Point Updates in Basic Jacobi Iteration
Damping of Eigenfunctions of Short and Long Wavelength
Extension of Jacobi Eigenvalue Analysis to two or more Dimensions
Direct Solution Method for Ax=b
Banded Matrix Computational Complexity
Comparison of Computational Complexity between Direct and Iterative Methods
Memory Use in Direct and Iterative Methods
Over Relaxation (SOR) and Relation to Jacobi and Gauss-Seidel
Over Relaxation Eigenvalues and Matrices for Jacobi Iteration
Jacobi Iteration Eigenvalues as a function of Over Relaxation Parameter
Jacobi Relaxation for Over Relaxation Parameter w =1/2
Introduction to Gauss-Seidel Iterative Approach 
6:Mathematical and Pseudo Code Form of Gauss Seidel Iteration Method 7:Mathematical (Matrix) Form of Gauss Seidel 8:Parallelism in Gauss-Seidel Iteration 9:Matrix Example Stencil 10:Matrix---Wavefront Parallelism for Gauss Seidel 11:The Red-Black Two Phase Parallel Gauss Seidel Iteration 12:Analysis of Parallel Red Black Gauss Seidel 13:Eigenvalues of Gauss Seidel Iteration Matrix 14:Comparison of Convergence of Gauss-Seidel and Jacobi Iteration 15:Successive Overrelaxation Iteration Method (SOR) 16:Convergence of SOR Compared to Jacobi and Gauss Seidel 17:Estimate of Over Relaxation Parameter 18:Pseudo Code for SOR---Successive Over Relaxation Full WebWisdom URL and this Foilset Search
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