testcollocpotro.m

本代码为基于matlab的求解偏微分方程的利用径向基函数的无网格方法的源码

% This is the test driver for the potential collocation problem.
% Not yet finished, work in progress.
% Before starting this program, please run Collocation.m to define the global
% variables
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% generate boundary and interior points
if RBFdomain==7
    domaincreator %m-file
    intpoints=[intpoints;bndpoints];                 % use boundary points also as "interior"
else
bndpoints=regbndpointsRO(RBFstepsize);   
intpoints=[regintpointsRO(RBFstepsize) ; bndpoints]; % use boundary points also as "interior"
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% plot points, for checking
figure(2) ; 
cla
plot(intpoints(:,1),intpoints(:,2),'.')
axis equal
hold on
plot(bndpoints(:,1),bndpoints(:,2),'O');
title('Collocation Points');
hold off;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[nint,nintdim]=size(intpoints);
intvalues=zeros(nint,1);                                % rhs values in interior
bndvalues=fct2D(bndpoints(:,1),bndpoints(:,2));         % rhs values on boundary
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% solve the linear system
result = rbfLapsolvecond (intpoints, intvalues, bndpoints, bndvalues); 
coeff=result{1};
condition=result{2};
handel=findobj('Tag','text3');
set(handel,'String',['Condition of matrix: ',num2str(condition)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% now evaluate the solution at given boundary points, data must be reproduced  
bndrepvalues = rbfPeval (bndpoints, intpoints, bndpoints, coeff);
bnderrnorm=max(bndrepvalues-bndvalues); % should be small
handel=findobj('Tag','text4');
set(handel,'String',['largest error at boundary collocation  points: ',num2str(bnderrnorm)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(3)   % now test for some more boundary points
cla
if RBFdomain==7
    bndtestpoints=onpolygon(RBFstepsize.*0.05,vertex);
else
bndtestpoints=regbndpointsRO(RBFstepsize.*0.05);
end
% now evaluate the solution at the boundary 
bndrepvalues = rbfPeval (bndtestpoints, intpoints, bndpoints, coeff);
plot(bndrepvalues-fct2D(bndtestpoints(:,1),bndtestpoints(:,2))); % plots error on boundary 
title('Error on boundary');
hold off;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% now evaluate the Laplacian of the solution at given interior points, data must be reproduced  
intrepvalues = rbfLPeval (intpoints, intpoints, bndpoints, coeff);
interrnorm=max(intrepvalues-intvalues); % should be small
handel=findobj('Tag','text5');
set(handel,'String',['largest error of the Laplacian at  interior  collocation points: ',num2str(bnderrnorm)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% now we create a fine grid 
np=3*ceil(2/RBFstepsize);
[X,Y]=meshgrid(-1:2/(np-1):1,-1:2/(np-1):1);
xr=reshape(X,[(np)*(np) 1]);
yr=reshape(Y,[(np)*(np) 1]);
datapoints=[xr yr];
if RBFdomain==7
   in=inpolygon(X,Y,vertex(:,1),vertex(:,2));
mask=in==1;
else
    in=domainfct(X,Y);
    mask=in<=0;
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% now we evaluate the approximation on a fine grid 
figure(4) 
cla
datarepvalues = rbfPeval (datapoints, intpoints, bndpoints, coeff);
surfc(X,Y,mask.*reshape(datarepvalues,[np np]));
shading interp;
hold on
title('the plot shows the approximation inside the domain');
hold off
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% now we evaluate the Laplacian of the approximation on a fine grid 
figure(5) 
cla
datarepvalues = rbfLPeval (datapoints, intpoints, bndpoints, coeff);
surfc(X,Y,mask.*reshape(datarepvalues,[np np]));
shading interp;
hold on
title('the plot shows: Laplace[approximation] inside the domain');
handel=findobj('Tag','text6');
error=max(max(abs(mask.*reshape(datarepvalues,[np np]))));
set(handel,'String',['largest value  of Laplacian  inside the domain    : ',num2str(error)]);
hold off;
handel=findobj('Tag','text7');
set(handel,'String','');
figure(6)