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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 |
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Delivered Lectures for CPS615 -- Base Course for the Simulation Track of Computational Science
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Abstract of Nov 26 1996 CPS615 Lecture
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24:Example for Two-Dimensional Triangular Elements
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25:Bilinear Form of Integral with Triangular Elements
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26:Formula for Stiffness Matrix Element
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27:Finite Element Equations
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28:Structure of Stiffness Matrix and Its Assembly
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29:Conditions on Triangulation
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30:Introduction to Poor Person's Conjugate Gradient
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31:Conjugate Gradient Iteration for Quadratic Form
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32:Conjugate Gradient and Method of Steepest Descent
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33:Conjugate Gradient for Finite Element Problems
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34:Poor Person's Conjugate Gradient and Eigenvalues of Matrix
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35:Diagonalization of Quadratic Form
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36:Diagonalization of Conjugate Gradient Equations
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37:Convergence of Conjugate Gradient in Diagonalized Form
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36:Diagonalization of Conjugate Gradient Equations
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38:Clarification of Eigenvalue Analysis for Conjugate Gradient and Jacobi Iteration
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39:Intuitive Description of Poor Person's Conjugate Gradient Algorithm
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40:Improvement of Poor Person's Conjugate Gradient with Orthonormal Iteration
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41:Full Conjugate Gradient Algorithm
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42:Overview of Parallelism in Conjugate Gradient
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43:Parallel Issues in Calculation of Matrix Elements
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44:Scalar Products in Parallel Conjugate Gradient
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45:Preconditioning in Conjugate Gradient
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46:Convergence of Conjugate Gradient Full WebWisdom URL and this Foilset Search
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