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CPS615 Finite Element and Conjugate Gradient Presentation
Given by Geoffrey C. Fox at CPS615 Fall Semester 95 Simulation Track on 18 November 95. Foils prepared 8 Nov 1995
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This derives the finite element method for a simple two dimensional Laplacian with triangular elements
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We use this to motivate conjugate gradient as a variant of steepest descent for variational principle underlying FEM
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We discuss preconditioning, parallelism and convergence of general conjugate gradient method
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This mixed presentation uses parts of the following base foilsets which can also
be looked at on their own!
CPS615-Master95 Miscellaneous CPS615 Foils
CPS615FEMetc95 CPS615 Foils on Finite Element Methods, Gauss
Seidel, Conjugate Gradient and Differential
Operators
CPS615-Master95 005 001 CPS615 -- Base Course for the
Simulation Track of Computational
Science
Fall Semester 1995 --
Finite Element Methods and Conjugate
Gradient Methods
CPS615-Master95 006 002 Abstract of CPS615 Finite
Element/Conjugate Gradient
Presentation
CPS615FEMetc95 019 003 19:Integral Formulation of Finite
Element Method
CPS615FEMetc95 020 004 20:Variation in Integral
CPS615FEMetc95 021 005 21:Equivalence of Integral and
Differential Formulation of
Laplace's Equation
CPS615FEMetc95 022 006 22:Discretization of Integral
CPS615FEMetc95 023 007 23:Triangular Elements in Two
Dimensions
CPS615FEMetc95 024 008 24:Example for Two-Dimensional
Triangular Elements
CPS615FEMetc95 025 009 25:Bilinear Form of Integral with
Triangular Elements
CPS615FEMetc95 026 010 26:Formula for Stiffness Matrix
Element
CPS615FEMetc95 027 011 27:Finite Element Equations
CPS615FEMetc95 028 012 28:Structure of Stiffness Matrix
and Its Assembly
CPS615FEMetc95 029 013 29:Conditions on Triangulation
CPS615FEMetc95 030 014 30:Introduction to Poor Person's
Conjugate Gradient
CPS615FEMetc95 031 015 31:Conjugate Gradient Iteration for
Quadratic Form
CPS615FEMetc95 032 016 32:Conjugate Gradient and Method of
Steepest Descent
CPS615FEMetc95 033 017 33:Conjugate Gradient for Finite
Element Problems
CPS615FEMetc95 034 018 34:Poor Person's Conjugate Gradient
and Eigenvalues of Matrix
CPS615FEMetc95 035 019 35:Diagonalization of Quadratic Form
CPS615FEMetc95 036 020 36:Diagonalization of Conjugate
Gradient Equations
CPS615FEMetc95 037 021 37:Convergence of Conjugate Gradient
in Diagonalized Form
CPS615FEMetc95 038 022 38:Clarification of Eigenvalue
Analysis for Conjugate Gradient
and Jacobi Iteration
CPS615FEMetc95 039 023 39:Intuitive Description of Poor
Person's Conjugate Gradient
Algorithm
CPS615FEMetc95 040 024 40:Improvement of Poor Person's
Conjugate Gradient with Orthonormal
Iteration
CPS615FEMetc95 041 025 41:Full Conjugate Gradient Algorithm
CPS615FEMetc95 042 026 42:Overview of Parallelism in
Conjugate Gradient
CPS615FEMetc95 043 027 43:Parallel Issues in Calculation
of Matrix Elements
CPS615FEMetc95 044 028 44:Scalar Products in Parallel
Conjugate Gradient
CPS615FEMetc95 045 029 45:Preconditioning in Conjugate
Gradient
CPS615FEMetc95 046 030 46:Convergence of Conjugate Gradient
List of Foils Used as they occur
CPS615-Master95 Miscellaneous CPS615 Foils
5 6
CPS615FEMetc95 CPS615 Foils on Finite Element Methods, Gauss
Seidel, Conjugate Gradient and Differential
Operators
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
Sorted List of Foils Used
CPS615-Master95 Miscellaneous CPS615 Foils
5 6
CPS615FEMetc95 CPS615 Foils on Finite Element Methods, Gauss
Seidel, Conjugate Gradient and Differential
Operators
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
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