Transcription of Partial Differential Equation Toolbox User's Guide
1 ComputationVisualizationProgrammingParti al Differential EquationToolboxFor Use with matlab User s GuideComputer Solutions Europe ABHow to Contact The MathWorks:508-647-7000 Phone508-647-7001 FaxThe MathWorks, Prime Park WayNatick, MA 01760-1500 FTP Technical Product enhancement Bug Documentation error Subscribing user Order status, license renewals, Sales, pricing.
2 And general informationPartial Differential Equation Toolbox User s Guide COPYRIGHT 1984 - 1997 by The MathWorks, Inc. All Rights software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-duced in any form without prior written consent from The MathWorks, GOVERNMENT: If Licensee is acquiring the Programs on behalf of any unit or agency of the Government, the following shall apply: (a) For units of the Department of Defense.
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4 August 1995 First printingFebruary 1996 Reprint%FAX)@iContents1 TutorialIntroduction ..1-2 What Does this Toolbox Do? ..1-2 Can I Use the PDE Toolbox ? .. 1-2 What Problems Can I Solve? ..1-3In Which Areas Can the Toolbox Be Used? ..1-5 How Do I Define a PDE Problem? ..1-5 How Can I Solve a PDE Problem? ..1-6 Can I Use the Toolbox for Nonstandard Problems? ..1-6 How Can I Visualize My Results? ..1-6 Are There Any Applications Already Implemented? ..1-7 Can I Extend the Functionality of the Toolbox ? ..1-7 How Can I Solve 3-D Problems by 2-D Models?
5 1-8 Getting Started ..1-9 Basics of The Finite Element Method ..1-18 Using the Graphical User Interface ..1-23 The PDE Toolbox Graphical User Interface ..1-23 The Menus ..1-24 The Toolbar ..1-25 The GUI Modes ..1-26 The CSG Model and the Set Formula ..1-27 Creating Rounded Corners ..1-28 Suggested Modeling Method ..1-31 Object Selection Methods ..1-35 Display Additional Information ..1-35 Entering Parameter Values as matlab Expressions ..1-36 Using PDE Toolbox version Model M-files ..1-36iiContentsUsing Command-Line Functions.
6 1-37 Data Structures and Utility Functions .. 1-37 Constructive Solid Geometry Model .. 1-38 Decomposed Geometry .. 1-39 Boundary Conditions .. 1-39 Equation Coefficients .. 1-39 Mesh .. 1-39 Solution .. 1-40 Post Processing and Presentation .. 1-40 Hints and Suggestions for Using Command-Line Functions .. 1-402 ExamplesExamples of Elliptic Problems .. 2-2 Poisson s Equation on Unit Disk .. 2-2 Using the Graphical User Interface .. 2-2 Using Command-Line Functions .. 2-4A Scattering Problem .. 2-6 Using the Graphical User Interface.
7 2-8A Minimal Surface Problem .. 2-10 Using the Graphical User Interface .. 2-10 Using Command-Line Functions .. 2-11 Domain Decomposition .. 2-12 Examples of Parabolic Problems.. 2-16 The Heat Equation : A Heated Metal Block .. 2-16 Using the Graphical User Interface .. 2-17 Using Command-Line Functions .. 2-19 Heat Distribution in Radioactive Rod .. 2-21 Using the Graphical User Interface .. 2-22 Examples of Hyperbolic Problems .. 2-23 The Wave Equation .. 2-23 Using the Graphical User Interface .. 2-23 Using Command-Line Functions.
8 2-25iiiExamples of Eigenvalue Problems .. 2-27 Eigenvalues and Eigenfunctions for the L-Shaped Membrane.. 2-27 Using the Graphical User Interface .. 2-27 Using Command-Line Functions .. 2-28L-Shaped Membrane with Rounded Corner .. 2-31 Eigenvalues and Eigenmodes of a Square .. 2-32 Using the Graphical User Interface .. 2-33 Using Command-Line Functions .. 2-33 Application Modes .. 2-35 The Application Modes and the GUI .. 2-35 Structural Mechanics - Plane Stress .. 2-36 Example .. 2-39 Using the Graphical User Interface .. 2-39 Structural Mechanics - Plane Strain.
9 2-41 Electrostatics .. 2-43 Example .. 2-44 Using the Graphical User Interface .. 2-44 Magnetostatics .. 2-46 Example .. 2-47 Using the Graphical User Interface .. 2-48AC Power Electromagnetics .. 2-51 Example .. 2-52 Using the Graphical User Interface .. 2-53 Conductive Media DC .. 2-55 Example .. 2-55 Using the Graphical User Interface .. 2-56 Heat Transfer .. 2-57 Example .. 2-58 Using the Graphical User Interface .. 2-59 Diffusion .. 2-61ivContents3 The Graphical User InterfacePDE Toolbox Menus .. 3-3 File Menu .. 3-3 New.
10 3-3 Open .. 3-4 Save As .. 3-5 Print .. 3-6 Edit Menu .. 3-7 Paste .. 3-8 Options Menu .. 3-9 Grid Spacing .. 3-10 Axes Limits .. 3-11 Application .. 3-11 Draw Menu .. 3-13 Rotate .. 3-14 Boundary Menu .. 3-15 Specify Boundary Conditions .. 3-16 PDE Menu .. 3-18 PDE Specification .. 3-19 Mesh Menu .. 3-22 Parameters .. 3-23 Solve Menu .. 3-25 Parameters .. 3-25 Plot Menu .. 3-30 Parameters .. 3-30 Additional Plot Control Options .. 3-34 Window Menu .. 3-37 Help Menu .. 3-37 The Toolbar .. 3-38v4 The Finite Element MethodThe Elliptic Equation .
