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CPS615-Basic PDE Solver Discussion and Sparse Matrix Formulation
Given by Geoffrey C. Fox at Delivered Lectures of CPS615 Basic Simulation Track for Computational Science on 8 November 96. Foils prepared 11 November 1996
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This starts basic module on Partial Differential Solvers with
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Introduction to Classification of Equations
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Basic Discretization
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Derivation of Sparse Matrix Formulation
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Analogies of Iteration with Artificial Time
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Start of Explicit Matrix Formulation for Simple Cases
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This mixed presentation uses parts of the following base foilsets which can also
be looked at on their own!
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
CPS615-95G CPS615 Foils -- Master set G for
Iterative Approachs to PDE Solution
CPS 615 Lectures 1996 Fall Semester -- November 8
Introduction to PDE's
CPS615Master96 073 001 Delivered Lectures for
CPS615 -- Base Course for
the Simulation Track of
Computational Science
Fall Semester 1996 --
Lecture of November 8 - 1996
CPS615Master96 078 002 Abstract of Nov 8 1996
CPS615 Lecture
CPS615-95G 002 003 Abstract of PDE and
Iterative Solver CPS615
Module
Introduction to PDE's and their Classification
CPS615-95G 003 004 Partial Differential
Equations: Use in Continuum
Physics
Examples and basic Notation
CPS615-95G 004 005 Examples of Different Types
of Partial Differential
Equations:
The Wave Equation
(Hyperbolic) and Typical One
Dimensional Solution
CPS615-95G 005 006 Examples of Different Types
of Partial Differential
Equations:
The Parabolic Equation
CPS615-95G 006 007 Examples of Different Types
of PDE's: Laplace and
Poisson Elliptic Equations
CPS615-95G 007 008 What Conditions are
sufficient for solution of
PDE's -- Cauchy Boundary
Conditions and
Hyperbolic,Parabolic and
Elliptic PDE's
CPS615-95G 008 009 Closed Boundaries; Dirichlet
and Neumann Conditions
Summary of what PDE Types
have What Boundary
Conditions
CPS615-95G 009 010 Examples of Open(Diffusion)
and Closed(Laplace) Boundary
Conditions
Discretization of Laplace's equation and Sparse Matrix Form
CPS615-95G 010 011 Solutions to Elliptic
Equations by Finite
Differences
CPS615-95G 011 012 Central Difference Operator
with error O(h2)
CPS615-95G 012 013 Difference Equation form of
the Operator to solve
Laplace's equation
CPS615-95G 013 014 The 12 by 12 Block
Tridiagonal Equations Coming
from Laplace's Equation on
a Tiny 5 by 6 Grid
CPS615-95G 014 015 General Form of Sparse
Matrix Coming from Laplace's
Equation - I
CPS615-95G 015 016 General Form of Sparse
Matrix Coming from Laplace's
Equation in two dimensions
- II
Artificial Time Motivation of Iteration
CPS615-95G 016 017 Iterative Methods and
Analogy to Diffusion with an
Artificial Time
CPS615-95G 017 018 Solution of Artificial Time
Equation as a Diffusion
System Discretized in Space
and Time
CPS615-95G 018 019 General 2D Artificial Time
Diffusion Equation in
Iterative Form
CPS615-95G 019 020 Traditional Iterative
Methods as Special Cases of
Artificial Time Diffusion
Formalism
General Formulation of Iterative Solvers
CPS615-95G 020 021 Simple Iterative Methods:
Jacobi, Gauss-Seidel, SOR
CPS615-95G 021 022 Matrix Notation for
Iterative Methods
List of Foils Used as they occur
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
73 78
CPS615-95G CPS615 Foils -- Master set G for
Iterative Approachs to PDE Solution
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Sorted List of Foils Used
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
73 78
CPS615-95G CPS615 Foils -- Master set G for
Iterative Approachs to PDE Solution
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
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