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Akhtar Jan
Akhtar Jan 2022-3-9
评论： Akhtar Jan 2022-3-9
shape = 2.5;
N = 30;
Np = N^2;
[X,Y] = meshgrid(linespace(0,1,N),linespace(0,1,N));
x = reshape(X,N^2,1);
y = reshape(Y,N^2,1);
f = -2*(2*y.^3-3*y.^2+1)+6*(1-x.^2).*(2*y-1);
u = (1-x.^2).*(2*y.^3-3*y.^2+1); % exact solution
H = zeros(Np,Np);
rx = zeros(Np,Np);
ry = zeros(Np,Np);
r = zeros(Np,Np);
dirichletBCs = find(x==0 | x==1); % identify boundry and interior centers
neumannBCs = find ((y==0 | y==1)& ~(x==0 | x==1));
interior = find('x~=0' & 'x~ = 1' & 'y~ = 0' & 'y~ = 1' );
f (dirichletBCs)=u(dirichletBCs);
f (neumannBCs)= 0;
for i =1:Np
for j =1:Np
rx ( i , j ) = x ( i )-x ( j ) ;
ry ( i , j ) = y ( i )-y ( j ) ;
r ( i , j ) = sqrt ( rx ( i , j )^2 + ry ( i , j )^2 );
end
end
H(dirichletBCs,:)=mq(r(dirichletBCs,:),shape); % e v a l u a t i on matrix
H(neumannBCs,:)= mqDerivatives(r(neumannBCs,:),ry(neumannBCs,:),shape,1);
Hxx = mqDerivatives(r(interior,:),rx(interior,:),shape,2);
Hyy = mqDerivatives(r(interior,:),ry(interior,:),shape,2);
H(interior,:)=Hxx+Hyy;
kappa=cond(H);
alpha=H\f;
B = mq( r , shape ) ; % system matrix
uh = B*alpha;
error = norm(uh-u,inf);
t = delaunay(x,y);trisurf(t,x,y,abs(uh-u));
xlabel 'x' , ylabel 'y' colormap('Summer')

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回答（1 个）

DGM
DGM 2022-3-9
I can't test anything, since there are missing functions, but:
% there is no linespace()
%[X,Y] = meshgrid(linespace(0,1,N),linespace(0,1,N));
[X,Y] = meshgrid(linspace(0,1,N),linspace(0,1,N));
% this is an inexplicable misuse of char vectors and invalid operator spacing
%interior = find('x~=0' & 'x~ = 1' & 'y~ = 0' & 'y~ = 1' );
interior = find(x~=0 & x~=1 & y~=0 & y~=1 );
% using command syntax for xlabel,ylabel is technically valid
% but the line continuation will cause an error at colormap()
%xlabel 'x' , ylabel 'y' colormap('Summer')
xlabel('x')
ylabel('y')
colormap('Summer')
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DGM
DGM 2022-3-9
Unless you're declaring that you've given up, you'll have to explain what exactly you did and what the observed outcomes were. If there are errors, show them. Do you have the functions mq() and mqDerivatives()? I don't.
You are the only person who has access to the information necessary to troubleshoot the problem.

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