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assert(version>=2.23);
// Mortar (4 sub domain)
// with matrix -et Precon Conjugade Gradient --
// Neuman -> Dirichlet .
// -------------------------------
func f=1+x+y;
real g=1;
int withprecon=1;
macro Grad(u) [ dx(u), dy(u) ] //
int nbsd=4;
macro Psd(U) U[0],U[1],U[2],U[3] //
int labext= nbsd+1;
real meshsize=0.025;
real meshsizem=meshsize*1.5;
bool noconforme=0;
include "mortar-msh.idp"
cout << "mortar : " << endl;
mesh Thm=Tha;
Thm=adaptmesh(Thm,meshsizem,IsMetric=1,thetamax=60,nbvx=100000);
Thm=adaptmesh(Thm,meshsizem,IsMetric=1,thetamax=60,nbvx=1000000);
Thm=emptymesh(Thm);
mesh Thmm=Thm;
if(noconforme)
{ // need a find mesh to integrate on Thm.
Thmm=trunc(Thm,split=4,1); // for fine integration
Thmm=emptymesh(Thmm);
}
plot(Thm,wait=0);
verbosity=1;
mesh[int] Thsd(nbsd);
for(int sd=0;sd<nbsd;++sd)
Thsd[sd]=trunc(Tha,region==regi[sd],split=1);// les sous domaines
if(noconforme)
{
for(int sd=0;sd<nbsd;++sd)
Thsd[sd]=adaptmesh(Thsd[sd],meshsize*(1+sd*0.05),IsMetric=1,nbvx=100000,thetamax=60);// les sous domaines
}
plot(Thsd,Thm);
// a faire : plot(Thsd,Thm,wait=1);
fespace Lh(Thm,P1);
fespace RTh(Thm,[P0edge,P0edge]);
RTh [Nmx,Nmy]; // ne marche pas car la normal
// n'est definie que une un bord
varf vNN([ux,uy],[nx,ny]) = int1d(Thm,1)(( nx*N.x + ny*N.y)/lenEdge);
Nmx[]= vNN(0,RTh);
// les joint P0 sur le squelette
// ----- \int [q] l + \int[p] m
Lh lh=0,rhsl=0;
mesh Thi=Thsd[0];
// remark: operator # is the concatenation operator in macro
// cout << " Domaine " << i<< " --------" << endl;
// OK P1/P0 ;, PB P1/P1, P1/P0Edge , FH..
fespace Vhi(Thi,P1);
fespace Ehi(Thi,P0);
matrix[int] Asd(nbsd),Csd(nbsd),PAsd(nbsd),PIsd(nbsd),PJsd(nbsd);
Vhi[int] usd(nbsd),vsd(nbsd),rhssd(nbsd), pusd(nbsd),bcsd(nbsd);
Ehi[int] epssd(nbsd);
real tgv=1e30;
for(int sd=0;sd<nbsd;++sd)
{
varf cci([l],[u]) = int1d(Thmm,1,qforder=3)(l*u*epssd[sd]);
varf vepsi(u,v)= int1d(Thi,1,qforder=10)( (Nmx*N.x + Nmy*N.y)*v/lenEdge);
varf vLapMi([ui],[vi],tgv=tgv) =
int2d(Thi)( Grad(ui)'*Grad(vi) )
// + int1d(Thi,1,qfe=qf1pElump)(alpha*ui*vi)
+ int2d(Thi) (f*vi) + on(labext,ui=g);
varf vPLapMi([ui],[vi],tgv=tgv) =
int2d(Thi)( Grad(ui)'*Grad(vi) )
// + int1d(Thi,1,qfe=qf1pElump)(alphap*ui*vi)
+ on(labext,1,ui=0);
;
varf vrhsMi(ui,vi) = on(labext,ui=g);
Thi=Thsd[sd];
usd[sd]=0;
vsd[sd]=0;
epssd[sd][]= vepsi(0,Ehi);
epssd[sd] = -real(epssd[sd] <-0.00001) + real(epssd[sd] >0.00001);
Csd[sd] = cci(Lh,Vhi);
Asd[sd] = vLapMi(Vhi,Vhi,solver=UMFPACK);
PAsd[sd] = vPLapMi(Vhi,Vhi,solver=UMFPACK);
matrix IVL=interpolate(Vhi,Lh,inside=1);
// v = IVL*l
varf vonext(u,v)=on(labext,u=1);
varf von1(u,v)=on(1,u=1);
real[int] onext=vonext(0,Vhi);
real[int] on1=von1(0,Vhi);
on1= on1 ? 1 : 0;
on1 = onext ? 0 : on1; // remove df of ext
matrix I1(on1);// matrix tgv $i\in Gamma_1 \ Gamma_e $ , 0 otherwise
PIsd[sd]= I1*IVL;// remove of line not on $Gamma_1 \ Gamma_e $
// so PIsd[sd]*l = tgv * Interpole l on $Gamma_1 \ Gamma_e $
I1.diag=on1;
matrix AA=I1*Asd[sd];// remove line not on lab 1
PJsd[sd]= IVL'*AA;
rhssd[sd][]=vLapMi(0,Vhi);
}
plot(epssd,cmm="eps 0,1,2,3",wait=0,value=1);
lh[]=0;
varf vDD(u,v) = int2d(Thm)(u*v*1e-10);
varf vML(u,v) = int2d(Thm)(u*v*1e-10)+int1d(Thm,1)(u*v);
matrix ML=vML(Lh,Lh);
matrix DD=vDD(Lh,Lh);
matrix M=[
[ Asd[0] ,0 ,0 ,0 ,Csd[0] ],
[ 0 ,Asd[1] ,0 ,0 ,Csd[1] ],
[ 0 ,0 ,Asd[2] ,0 ,Csd[2] ],
[ 0 ,0 ,0 ,Asd[3] ,Csd[3] ],
[ Csd[0]',Csd[1]',Csd[2]',Csd[3]',DD ]
];
real[int] xx(M.n);
real[int] bb =[rhssd[0][], rhssd[1][],rhssd[2][],rhssd[3][],rhsl[] ];
set(M,solver=UMFPACK);
xx = M^-1 * bb;
[usd[0][],usd[1][],usd[2][],usd[3][],lh[]] = xx; // dispatch the solution
plot(usd,cmm="u1,u2,u3,u4",wait=1);
int itera=0;
varf vbc(u,v) = int1d(Thm,labext)(v);
real[int] lbc(Lh.ndof),lbc0(Lh.ndof);
lbc=vbc(0,Lh);
lbc = lbc ? 0 : 1 ;
func real[int] SkPb(real[int] &l)
{
int verb=verbosity; verbosity=0; itera++;
for(int sd=0;sd<nbsd;++sd)
{
Thi=Thsd[sd]; // for initialisation of vsd with the correct size
vsd[sd][] = rhssd[sd][];
vsd[sd][] += Csd[sd]* l;
usd[sd][] = Asd[sd]^-1*vsd[sd][];
}
l=0;
for(int sd=0;sd<nbsd;++sd)
l += Csd[sd]'*usd[sd][];
l= lbc .* l;
plot(usd,wait=0,cmm="CG iteration u");
verbosity=verb;
return l ;
};
func real[int] PSkPb(real[int] &l)
{
if(withprecon)
{
int verb=verbosity; verbosity=0; itera++;
real[int] ll= ML^-1*l;
ll= lbc .* ll;
ll *= tgv;
for(int sd=0;sd<nbsd;++sd)
{
Thi=Thsd[sd];
pusd[sd][] = PAsd[sd]^-1*(vsd[sd][]= PIsd[sd]* ll);
}
ll=0;
for(int sd=0;sd<nbsd;++sd)
ll += PJsd[sd]*pusd[sd][];
l = ML^-1*ll;
l= lbc .* l;
verbosity=verb;
}
return l ;
};
verbosity=100;
lh[]=0;
LinearCG(SkPb,lh[],eps=1.e-7,nbiter=100,precon=PSkPb);
verbosity=1;
plot(usd,wait=1,cmm="CG");
// FFCS: for regression tests
real regtest;
{
fespace Vha(Tha,P1);
Vha vah,uah;
solve vLapMM([uah],[vah]) =
int2d(Tha)( Grad(uah)'*Grad(vah) )
- int2d(Tha) (f*vah)
+ on(labext,uah=g)
;
verbosity =3;
plot(uah,usd,cmm="uah",wait=1);
regtest=uah[]'*uah[];
}
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