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CPS615-Finite Elements(Continued) and Conjugate Gradient
Given by Geoffrey C. Fox at Delivered Lectures of CPS615 Basic Simulation Track for Computational Science on 26 November 96. Foils prepared 29 December 1996
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This covers essentially all the finite element method and its solution using the conjugate gradient method
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Only the simple 2D Laplace equation using triangular nodes is discussed
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We stress variational method as an optimization method and you use this analogy to motivate conjugate gradient as an improved steepest descent approach
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We discuss parallel computing issues for both finite element and conjugate gradient
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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
CPS615FEMetc95 CPS615 Foils on Finite Element
Methods, Gauss Seidel, Conjugate
Gradient and Differential Operators
CPS 615 Lectures 1996 Fall Semester -- November 26
CPS615Master96 082 001 Delivered Lectures for
CPS615 -- Base Course for
the Simulation Track of
Computational Science
Fall Semester 1996 --
Lecture of November 26 -
1996
CPS615Master96 085 002 Abstract of Nov 26 1996
CPS615 Lecture
Finite Element Methods
CPS615FEMetc95 024 003 24:Example for
Two-Dimensional Triangular
Elements
CPS615FEMetc95 025 004 25:Bilinear Form of
Integral with Triangular
Elements
CPS615FEMetc95 026 005 26:Formula for Stiffness
Matrix Element
CPS615FEMetc95 027 006 27:Finite Element Equations
CPS615FEMetc95 028 007 28:Structure of Stiffness
Matrix and Its Assembly
CPS615FEMetc95 029 008 29:Conditions on
Triangulation
Conjugate Gradient Equations and Motivation
CPS615FEMetc95 030 009 30:Introduction to Poor
Person's Conjugate
Gradient
CPS615FEMetc95 031 010 31:Conjugate Gradient
Iteration for Quadratic
Form
CPS615FEMetc95 032 011 32:Conjugate Gradient and
Method of Steepest Descent
CPS615FEMetc95 033 012 33:Conjugate Gradient for
Finite Element Problems
CPS615FEMetc95 034 013 34:Poor Person's Conjugate
Gradient and Eigenvalues
of Matrix
CPS615FEMetc95 035 014 35:Diagonalization of
Quadratic Form
CPS615FEMetc95 036 015 36:Diagonalization of
Conjugate Gradient
Equations
CPS615FEMetc95 037 016 37:Convergence of Conjugate
Gradient in Diagonalized
Form
CPS615FEMetc95 036 017 36:Diagonalization of
Conjugate Gradient
Equations
CPS615FEMetc95 038 018 38:Clarification of
Eigenvalue Analysis for
Conjugate Gradient and
Jacobi Iteration
CPS615FEMetc95 039 019 39:Intuitive Description of
Poor Person's Conjugate
Gradient Algorithm
CPS615FEMetc95 040 020 40:Improvement of Poor
Person's Conjugate
Gradient with Orthonormal
Iteration
CPS615FEMetc95 041 021 41:Full Conjugate Gradient
Algorithm
Parallel Conjugate Gradient
CPS615FEMetc95 042 022 42:Overview of Parallelism
in Conjugate Gradient
CPS615FEMetc95 043 023 43:Parallel Issues in
Calculation of Matrix
Elements
CPS615FEMetc95 044 024 44:Scalar Products in
Parallel Conjugate
Gradient
CPS615FEMetc95 045 025 45:Preconditioning in
Conjugate Gradient
CPS615FEMetc95 046 026 46:Convergence of Conjugate
Gradient
List of Foils Used as they occur
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
82 85
CPS615FEMetc95 CPS615 Foils on Finite Element
Methods, Gauss Seidel, Conjugate
Gradient and Differential Operators
24 25 26 27 28 29 30 31 32 33 34 35 36 37 36 38 39 40 41 42 43 44 45 46
Sorted List of Foils Used
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
82 85
CPS615FEMetc95 CPS615 Foils on Finite Element
Methods, Gauss Seidel, Conjugate
Gradient and Differential Operators
24 25 26 27 28 29 30 31 32 33 34 35 36 36 37 38 39 40 41 42 43 44 45 46
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