Analysis of a Finite Element Method PDE/PROTRAN
This text can be used for two quite different purposes. It can be used as a reference book for the PDElPROTRAN user· who wishes to know more about the methods employed by PDE/PROTRAN Edition 1 (or its predecessor, TWODEPEP) in solving two-dimensional partial differential equations. However, because...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1985, 1985
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| Edition: | 1st ed. 1985 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Partial Differential Equation Applications
- 1.1 Energy Minimization
- 1.2 Mass Balance
- 1.3 Force Balance
- 1.4 Resonance
- 1.5 PDE/PROTRAN
- 1.6 Exercises
- 2. Elliptic Problems—Forming the Algebraic Equations
- 2.1 The Galerkin Method
- 2.2 Lagrangian Isoparametric Triangular Elements
- 2.3 Numerical Integration
- 2.4 Triangulation Refinement and Grading
- 2.5 Exercises
- 3. Elliptic Problems—Solving the Algebraic Equations
- 3.1 The Newton-Raphson Method
- 3.2 The Band Solver
- 3.3 The Frontal Solver
- 3.4 The Lanczos Solver
- 3.5 Exercises
- 4. Parabolic Problems
- 4.1 The Time Discretization
- 4.2 Stability
- 4.3 Solving the Linear Equations
- 4.4 Exercises
- 5. Hyperbolic problems
- 5.1 First Order Transport Problems
- 5.2 Second Order Wave Problems
- 5.3 Exercises
- 6. Eigenvalue Problems
- 6.1 The Rayleigh-Ritz Approximation
- 6.2 The Inverse Power Method
- 6.3 Exercises
- Appendices
- 1. Lanczos Iteration Properties
- 2. The PROTRAN Preprocessor
- 3. PDE/PROTRAN Keywords
- 4. Postscript