Full HTML for

Scripted foilset 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
Outside Index Summary of Material Secs 67.6

This covers essentially all the finite element method and its solution using the conjugate gradient method
Only the simple 2D Laplace equation using triangular nodes is discussed
We stress variational method as an optimization method and you use this analogy to motivate conjugate gradient as an improved steepest descent approach
We discuss parallel computing issues for both finite element and conjugate gradient

Table of Contents for full HTML of CPS615-Finite Elements(Continued) and Conjugate Gradient

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1 Delivered Lectures for CPS615 -- Base Course for the Simulation Track of Computational Science
Fall Semester 1996 --
Lecture of November 26 - 1996
2 Abstract of Nov 26 1996 CPS615 Lecture
3 24:Example for Two-Dimensional Triangular Elements
4 25:Bilinear Form of Integral with Triangular Elements
5 26:Formula for Stiffness Matrix Element
6 27:Finite Element Equations
7 28:Structure of Stiffness Matrix and Its Assembly
8 29:Conditions on Triangulation
9 30:Introduction to Poor Person's Conjugate Gradient
10 31:Conjugate Gradient Iteration for Quadratic Form
11 32:Conjugate Gradient and Method of Steepest Descent
12 33:Conjugate Gradient for Finite Element Problems
13 34:Poor Person's Conjugate Gradient and Eigenvalues of Matrix
14 35:Diagonalization of Quadratic Form
15 36:Diagonalization of Conjugate Gradient Equations
16 37:Convergence of Conjugate Gradient in Diagonalized Form
17 36:Diagonalization of Conjugate Gradient Equations
18 38:Clarification of Eigenvalue Analysis for Conjugate Gradient and Jacobi Iteration
19 39:Intuitive Description of Poor Person's Conjugate Gradient Algorithm
20 40:Improvement of Poor Person's Conjugate Gradient with Orthonormal Iteration
21 41:Full Conjugate Gradient Algorithm
22 42:Overview of Parallelism in Conjugate Gradient
23 43:Parallel Issues in Calculation of Matrix Elements
24 44:Scalar Products in Parallel Conjugate Gradient
25 45:Preconditioning in Conjugate Gradient
26 46:Convergence of Conjugate Gradient

Outside Index Summary of Material

HTML version of Scripted Foils prepared 29 December 1996

Foil 1 Delivered Lectures for CPS615 -- Base Course for the Simulation Track of Computational Science
Fall Semester 1996 --
Lecture of November 26 - 1996

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 67.6
Geoffrey Fox
NPAC
Room 3-131 CST
111 College Place
Syracuse NY 13244-4100
HTML version of Scripted Foils prepared 29 December 1996

Foil 2 Abstract of Nov 26 1996 CPS615 Lecture

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 67.6
This covers essentially all the finite element method and its solution using the conjugate gradient method
Only the simple 2D Laplace equation using triangular nodes is discussed
We stress variational method as an optimization method and you use this analogy to motivate conjugate gradient as an improved steepest descent approach
We discuss parallel computing issues for both finite element and conjugate gradient
HTML version of Scripted Foils prepared 29 December 1996

Foil 3 24:Example for Two-Dimensional Triangular Elements

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 74.8
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 4 25:Bilinear Form of Integral with Triangular Elements

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 239
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 5 26:Formula for Stiffness Matrix Element

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 61.9
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 6 27:Finite Element Equations

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 169.9
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 7 28:Structure of Stiffness Matrix and Its Assembly

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 116.6
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 8 29:Conditions on Triangulation

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 275
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 9 30:Introduction to Poor Person's Conjugate Gradient

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 223.2
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 10 31:Conjugate Gradient Iteration for Quadratic Form

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 440.6
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 11 32:Conjugate Gradient and Method of Steepest Descent

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 59
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 12 33:Conjugate Gradient for Finite Element Problems

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 92.1
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 13 34:Poor Person's Conjugate Gradient and Eigenvalues of Matrix

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 259.2
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 14 35:Diagonalization of Quadratic Form

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 172.8
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 15 36:Diagonalization of Conjugate Gradient Equations

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 141.1
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 16 37:Convergence of Conjugate Gradient in Diagonalized Form

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 69.1
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 17 36:Diagonalization of Conjugate Gradient Equations

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 120.9
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 18 38:Clarification of Eigenvalue Analysis for Conjugate Gradient and Jacobi Iteration

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 133.9
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 19 39:Intuitive Description of Poor Person's Conjugate Gradient Algorithm

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 305.2
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 20 40:Improvement of Poor Person's Conjugate Gradient with Orthonormal Iteration

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 80.6
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 21 41:Full Conjugate Gradient Algorithm

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 324
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 22 42:Overview of Parallelism in Conjugate Gradient

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 491
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 23 43:Parallel Issues in Calculation of Matrix Elements

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 234.7
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 24 44:Scalar Products in Parallel Conjugate Gradient

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 338.4
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 25 45:Preconditioning in Conjugate Gradient

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 106.5
See Original Foil
HTML version of Scripted Foils prepared 29 December 1996

Foil 26 46:Convergence of Conjugate Gradient

From CPS615-Finite Elements(Continued) and Conjugate Gradient Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 26 November 96. *
Full HTML Index Secs 156.9
See Original Foil
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