MatLab偏微分方程工具箱使用手册.pdf

发布时间：2022-05-30 发布人：admin 分类：说明书资料大小：3.02M 资料格式：pdf 举报版权申诉

第1页 / 共284页

第2页 / 共284页

第3页 / 共284页

第4页 / 共284页

第5页 / 共284页

第6页 / 共284页

第7页 / 共284页

第8页 / 共284页

Tutorial

Examples

The Graphical User Interface

The Finite Element Method

Reference

Index

Tutorial

Introduction

What Does this Toolbox Do?

Can I Use the PDE Toolbox?

What Problems Can I Solve?

In Which Areas Can the Toolbox Be Used?

How Do I Define a PDE Problem?

How Can I Solve a PDE Problem?

Can I Use the Toolbox for Nonstandard Problems?

How Can I Visualize My Results?

Are There Any Applications Already Implemented?

Can I Extend the Functionality of the Toolbox?

How Can I Solve 3-D Problems by 2-D Models?

Getting Started

Basics of The Finite Element Method

Using the Graphical User Interface

The PDE Toolbox Graphical User Interface

The Menus

The Toolbar

The GUI Modes

The CSG Model and the Set Formula

Creating Rounded Corners

Suggested Modeling Method

Object Selection Methods

Display Additional Information

Entering Parameter Values as MATLAB Expressions

Using PDE Toolbox version 1.0 Model M-files

Using Command-Line Functions

Data Structures and Utility Functions

Constructive Solid Geometry Model

Decomposed Geometry

Boundary Conditions

Equation Coefficients

Mesh

Solution

Post Processing and Presentation

Hints and Suggestions for Using Command-Line Funct...

Examples

Examples of Elliptic Problems

Poisson’s Equation on Unit Disk

Using the Graphical User Interface

Using Command-Line Functions

A Scattering Problem

Using the Graphical User Interface

A Minimal Surface Problem

Using the Graphical User Interface

Using Command-Line Functions

Domain Decomposition

Examples of Parabolic Problems

The Heat Equation: A Heated Metal Block

Using the Graphical User Interface

Using Command-Line Functions

Heat Distribution in Radioactive Rod

Using the Graphical User Interface

Examples of Hyperbolic Problems

The Wave Equation

Using the Graphical User Interface

Using Command-Line Functions

Examples of Eigenvalue Problems

Eigenvalues and Eigenfunctions for the L-Shaped Me...

Using the Graphical User Interface

Using Command-Line Functions

L-Shaped Membrane with Rounded Corner

Eigenvalues and Eigenmodes of a Square

Using the Graphical User Interface

Using Command-Line Functions

Application Modes

The Application Modes and the GUI

Structural Mechanics - Plane Stress

Example

Using the Graphical User Interface

Structural Mechanics - Plane Strain

Electrostatics

Example

Using the Graphical User Interface

Magnetostatics

Example

Using the Graphical User Interface

AC Power Electromagnetics

Example

Using the Graphical User Interface

Conductive Media DC

Example

Using the Graphical User Interface

Heat Transfer

Example

Using the Graphical User Interface

Diffusion

The Graphical User Interface

PDE Toolbox Menus

File Menu

New

Open . . .

Save As . . .

Print . . .

Edit Menu

Paste . . .

Options Menu

Grid Spacing . . .

Axes Limits . . .

Application

Draw Menu

Rotate . . .

Boundary Menu

Specify Boundary Conditions . . .

PDE Menu

PDE Specification . . .

Mesh Menu

Parameters . . .

Solve Menu

Parameters . . .

Plot Menu

Parameters . . .

Additional Plot Control Options

Window Menu

Help Menu

The Toolbar

The Finite Element Method

The Elliptic Equation

The Elliptic System

The Parabolic Equation

The Hyperbolic Equation

The Eigenvalue Equation

Nonlinear Equations

Adaptive Mesh Refinement

The Error Indicator Function

The Mesh Refiner

The Termination Criteria

Fast Solution of Poisson’s Equation

Reference

Commands Grouped by Function

PDE Algorithms

User Interface Algorithms

Geometry Algorithms

Plot Functions

Utility Algorithms

User Defined Algorithms

Demonstration Programs

adaptmesh

assema

assemb

assempde

PDE Coefficients for Scalar Case

PDE Coefficients for System Case

csgchk

csgdel

decsg

dst, idst

hyperbolic

initmesh

jigglemesh

parabolic

pdeadgsc

pdeadworst

pdearcl

pdebound

pdecgrad

pdecirc

pdecont

pdeeig

pdeellip

pdeent

pdegeom

pdegplot

pdegrad

pdeintrp

pdejmps

pdemdlcv

pdemesh

pdenonlin

pdeplot

pdepoly

pdeprtni

pderect

pdesdp, pdesde, pdesdt

pdesmech

pdesurf

pdetool

Boundary Condition Dialog Box

Model M-file

pdetrg

pdetriq

poiasma

poicalc

poiindex

poimesh

poisolv

refinemesh

sptarn

tri2grid

wbound

wgeom

Partial Differential Equation Toolbox For Use with MATLAB® Computer Solutions Europe AB Computation Visualization Programming User’s Guide

% FAX) @ How to Contact The MathWorks: 508-647-7000 508-647-7001 The MathWorks, Inc. 24 Prime Park Way Natick, MA 01760-1500 Phone Fax Mail http://www.mathworks.com ftp.mathworks.com comp.soft-sys.matlab support@mathworks.com suggest@mathworks.com bugs@mathworks.com doc@mathworks.com subscribe@mathworks.com service@mathworks.com info@mathworks.com Web Anonymous FTP server Newsgroup Technical support Product enhancement suggestions Bug reports Documentation error reports Subscribing user registration Order status, license renewals, passcodes Sales, pricing, and general information Partial Differential Equation Toolbox User’s Guide COPYRIGHT 1984 - 1997 by The MathWorks, Inc. All Rights Reserved. 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

1 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 MATLAB Expressions . . . . . . .1-36 Using PDE Toolbox version 1.0 Model M-files . . . . . . . . . . . . . .1-36 i

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 2 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 ii Contents

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 iii

3 The Graphical User Interface PDE Toolbox Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 File Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 New . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-38 iv Contents

4 The Finite Element Method The Elliptic Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 The Elliptic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 The Parabolic Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13 The Hyperbolic Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16 The Eigenvalue Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17 Nonlinear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21 Adaptive Mesh Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26 The Error Indicator Function . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26 The Mesh Refiner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27 The Termination Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28 Fast Solution of Poisson’s Equation . . . . . . . . . . . . . . . . . . . . 4-29 v

5 Reference Commands Grouped by Function . . . . . . . . . . . . . . . . . . . . . . . 5-3 PDE Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3 User Interface Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3 Geometry Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4 Plot Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4 Utility Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5 User Defined Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7 Demonstration Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7 PDE Coefficients for Scalar Case . . . . . . . . . . . . . . . . . . . . . 5-20 PDE Coefficients for System Case . . . . . . . . . . . . . . . . . . . . 5-21 Boundary Condition Dialog Box . . . . . . . . . . . . . . . . . . . . . . 5-80 Model M-file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-81 Index vi Contents

分享到：

赞收藏

资料库

MatLab偏微分方程工具箱使用手册.pdf

相关推荐

开发技术

热门标签

最新资料