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real r=0.25;
// a diamond with a hole
border a(t=0,1){x=-t+1; y=t;label=1;};
border b(t=0,1){ x=-t; y=1-t;label=2;};
border c(t=0,1){ x=t-1; y=-t;label=3;};
border d(t=0,1){ x=t; y=-1+t;label=4;};
border e(t=0,2*pi){ x=r*cos(t); y=-r*sin(t);label=0;};
int n = 10;
mesh Th= buildmesh(a(n)+b(n)+c(n)+d(n)+e(n));
plot(Th,wait=1);
real r2=1.732;
func abs=sqrt(x^2+y^2);
// warning for periodic condition:
// side a and c \hfilll
// on side a (label 1) $ x \in [0,1] $ or $ x-y\in [-1,1] $ \hfilll
// on side c (label 3) $ x \in [-1,0]$ or $ x-y\in[-1,1] $\hfilll
// so the common abcissa can be repectively $x$ and $x+1$
// or you can can try curviline abcissa $x-y$ and $x-y$
// 1 first way
// fespace Vh(Th,P2,periodic=[[2,1+x],[4,x],[1,x],[3,1+x]]);
// 2 second way
fespace Vh(Th,P2,periodic=[[2,x+y],[4,x+y],[1,x-y],[3,x-y]]);
Vh uh,vh;
func f=(y+x+1)*(y+x-1)*(y-x+1)*(y-x-1);
real intf = int2d(Th)(f);
real mTh = int2d(Th)(1.);
real moyf = intf/mTh;
cout << moyf << endl;
problem laplace(uh,vh) =
int2d(Th)( dx(uh)*dx(vh) + dy(uh)*dy(vh) ) + int2d(Th)( (moyf-f)*vh ) ;
laplace;
plot(uh,wait=1,ps="perio4.eps");
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