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Computation

Visualization

Programming

Partial Differential Equation

Toolbox

For Use with MATLAB

User’s Guide

Computer Solutions Europe AB

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Partial Differential Equation Toolbox User’s Guide



The 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, Inc

U.S. GOVERNMENT: If Licensee is acquiring the Programs on behalf of any unit or agency of the U.S.

Government, the following shall apply: (a) For units of the Department of Defense: the Government shall

have only the rights specified in the license under which the commercial computer software or commercial

software documentation was obtained, as set forth in subparagraph (a) of the Rights in Commercial

Computer Software or Commercial Software Documentation Clause at DFARS 227.7202-3, therefore the

rights set forth herein shall apply; and (b) For any other unit or agency: NOTICE: Notwithstanding any

other lease or license agreement that may pertain to, or accompany the delivery of, the computer software

and accompanying documentation, the rights of the Government regarding its use, reproduction, and disclo-

sure are as set forth in Clause 52.227-19 (c)(2) of the FAR.

MATLAB, Simulink, Handle Graphics, and Real-Time Workshop are registered trademarks and Stateflow

and Target Language Compiler are trademarks of The MathWorks, Inc.

Other product or brand names are trademarks or registered trademarks of their respective holders.

Printing History: August 1995 First printing

February 1996 Reprint

☎

FAX

✉

Contents

Tutorial

Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-2

What Does this Toolbox Do? . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-2

Can I Use the PDE Toolbox? . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-2

What Problems Can I Solve? . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-3

In 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? . . . . . . . . . . . . .

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 M

ATLAB

Expressions . . . . . . .

1-36

Using PDE Toolbox version 1.0 Model M-files . . . . . . . . . . . . . .

1-36

ii Contents

Using Command-Line Functions

. . . . . . . . . . . . . . . . . . . . . . .

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-40

Examples

Examples of Elliptic Problems

. . . . . . . . . . . . . . . . . . . . . . . . .

2-2

Poisson’s Equation on Unit Disk . . . . . . . . . . . . . . . . . . . . . . . . .

2-2

Using the Graphical User Interface . . . . . . . . . . . . . . . . . . . .

2-2

Using Command-Line Functions . . . . . . . . . . . . . . . . . . . . . .

2-4

A Scattering Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-6

Using the Graphical User Interface . . . . . . . . . . . . . . . . . . . .

2-8

A 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 . . . . . . . . . . . . . . . . . . . . .

2-25

iii

Examples 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 . . . . . . . . . . . . . . . . . . . . .

2-28

L-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 . . . . . . . . . . . . . . . . . . . .

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 . . . . . . . . . . . . . . . . . . .

2-48

AC 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-61

剩余283页未读，继续阅读

评论收藏

内容反馈

zjdyck

2012-08-17

要的就是英文版的，还行
zavierxu

2013-02-04

这个资料挺好的, 建议大家多看看
gonff

2014-05-26

这个工具很有用
oleolezx

2013-05-09

英文的。还不错
sogo3q

2014-02-04

不错，很全面

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