specifying the problem geometry：

ne=pdegeom d=pdegeom(bs) [x,y]=pdegeom(bs,s)

an example of how to create a cardioid.

ne=pdegeom is the number of edge segments.

d=pdegeom(bs) is a matrix with one column for each edge segment specified in bs.

Row 1 contains the start parameter value. Row 2 contains the end parameter value. Row 3 contains the label of the left-hand region (left with respect to direction induced by start and end from row 1 and 2). Row 4 contains the label of the right-hand region.

The complement of the union of all regions is assigned the region number 0.

[x,y]=pdegeom(bs,s) produces coordinates of edge segment points. bs specifies the edge segments and s the corresponding parameter values. bs can be a scalar.

注意： The parameter s should be approximately proportional to the curve length. All minimal regions should have at least two, and preferably three, edge segments in their boundary.

example：

The function cardg defines the geometry of a cardioid r = 2(1+cos(Φ)).

function [x,y]=cardg(bs,s) %CARDG Geometry File defining the geometry of a cardioid. nbs=4; if nargin==0 x=nbs; return end dl=[ 0 pi/2 pi 3*pi/2 pi/2 pi 3*pi/2 2*pi; 1 1 1 1 0 0 0 0]; if nargin==1 x=dl(:,bs); return end x=zeros(size(s)); y=zeros(size(s)); [m,n]=size(bs); if m==1 n==1, bs=bs*ones(size(s)); expand bs elseif m =size(s,1) n =size(s,2), error('bs must be scalar or of same size as s'); end nth=400; th=linspace(0,2*pi,nth); r=2*(1+cos(th)); xt=r.*cos(th); yt=r.*sin(th); th=pdearcl(th,[xt;yt],s,0,2*pi); r=2*(1+cos(th)); x(:)=r.*cos(th); y(:)=r.*sin(th);

We use the function pdearcl to make the parameter s proportional to arc length. You can test the function by typing:

» pdegplot('cardg'), axis equal » [p,e,t]=initmesh('cardg'); » pdemesh(p,e,t), axis equal

Then solve the PDE problem -Δu=1 on the geometry defined by the the cardioid. Use Dirichlet boundary conditions u = 0 . Finally plot the solution.

» u=assempde('cardb',p,e,t,1,0,1); » pdesurf(p,t,u);

m file补充

MATLAB可以执行存储在文件中的一系列语句。这样的文件被称为“m -file”，因为它们的扩展名必须是“.m"作为文件名。 m file可分为script files 和 function files

script file

由一系列普通的MATLAB语句组成。如果文件有文件名，如rotate.m，然后MATLAB命令rotate将导致执行文件中的语句。script file中的变量是全局变量，它将更改当前MATLAB会话环境中同名变量的值。 script file通常用于将数据输入到一个大的矩阵中，避免编辑输入的疏忽和错误。例如，在diskfile中输入data.m：

A = [ 1 2 3 4 5 6 7 8 ];

那么MATLAB语句data将执行data.m中的赋值。 一个m文件也可以引用其他m文件，包括递归地引用它自己。

function file

可以根据问题创建新的函数，这些函数将具有与其他MATLAB函数相同的状态。（函数文件中的变量默认为局部变量。但也可以将变量声明为全局变量。） 命名方式 函数名.m 第一行声明了函数名、输入参数和输出参数(区别于script file)。 A more general version of this function is given as follow:

function y = randint(m,n,a,b) % RANDINT Randomly generated integral matrix. % randint(m,n) returns an m-by-n such matrix with % entries between 0 and 9. % randint(m,n,a,b) returns entries between integers a and b. if nargin < 3, a=0; b=9; end y = floor((b-a+1)*rand(m,n))+a;

函数文件为randint.m。例如，MATLAB语句z = randint (4,5) 可将数字4和5是传递到变量m和n的function file，输出结果传递到变量z。由于变量在函数文件是局部的，在当前的MATLAB环境他们的名字是独立的。 注：使用nargin(“输入参数的数量”)允许为省略的输入变量设置默认值——比如上面示例中的a和b。

A function may also have multiple output arguments. For example:

function [mean, stdev] = stat(x) % STAT Mean and standard deviation % For a vector x, stat(x) returns the % mean and standard deviation of x. % For a matrix x, stat(x) returns two row % vectors containing, respectively, the % mean and standard deviation of each column. [m n] = size(x); if m == 1 m = n; % handle case of a row vector end mean = sum(x)/m; stdev = sqrt(sum(x.^2)/m -mean.^2);

将其放入磁盘文件stat.m后，例如，一个MATLAB命令**[xm, xd] = stat(x)**。将把向量x中的项的均值和标准偏差分别分配给xm和xd。对于具有多个输出参数的函数，也可以进行单个赋值。例如，xm = stat(x) (xm周围不需要括号)将把x的平均值分配给xm。