//---------------------------------------------------------
DMat& NDG2D::Lift2D()
//---------------------------------------------------------
{
// function [LIFT] = Lift2D()
// Purpose : Compute surface to volume lift term for DG formulation
DMat V1D,massEdge1,massEdge2,massEdge3; DVec faceR,faceS;
Index1D J1(1,Nfp), J2(Nfp+1,2*Nfp), J3(2*Nfp+1,3*Nfp);
DMat Emat(Np, Nfaces*Nfp);
// face 1
faceR = r(Fmask(All,1));
V1D = Vandermonde1D(N, faceR);
massEdge1 = inv(V1D*trans(V1D));
Emat(Fmask(All,1), J1) = massEdge1;
// face 2
faceR = r(Fmask(All,2));
V1D = Vandermonde1D(N, faceR);
massEdge2 = inv(V1D*trans(V1D));
Emat(Fmask(All,2), J2) = massEdge2;
// face 3
faceS = s(Fmask(All,3));
V1D = Vandermonde1D(N, faceS);
massEdge3 = inv(V1D*trans(V1D));
Emat(Fmask(All,3), J3) = massEdge3;
// inv(mass matrix)*\I_n (L_i,L_j)_{edge_n}
LIFT = V*(trans(V)*Emat);
return LIFT;
}
//---------------------------------------------------------
DMat& NDG3D::Lift3D()
//---------------------------------------------------------
{
// function [LIFT] = Lift3D(N, r, s, t)
// Purpose : Compute 3D surface to volume lift operator used in DG formulation
DMat Emat(Np, Nfaces*Nfp),VFace,massFace;
DVec faceR,faceS; IVec idr; Index1D JJ;
for (int face=1; face<=Nfaces; ++face) {
// process face
if (1==face) {faceR = r(Fmask(All,1)); faceS = s(Fmask(All,1));}
else if (2==face) {faceR = r(Fmask(All,2)); faceS = t(Fmask(All,2));}
else if (3==face) {faceR = s(Fmask(All,3)); faceS = t(Fmask(All,3));}
else if (4==face) {faceR = s(Fmask(All,4)); faceS = t(Fmask(All,4));}
VFace = Vandermonde2D(N, faceR, faceS);
massFace = inv(VFace*trans(VFace));
idr = Fmask(All,face);
//idc = (face-1)*Nfp+1: face*Nfp;
JJ.reset((face-1)*Nfp+1, face*Nfp);
//Emat(idr, JJ) = Emat(idr, JJ) + massFace;
Emat(idr, JJ) = massFace; // TW: += -> =
}
// inv(mass matrix)*\I_n (L_i,L_j)_{edge_n}
LIFT = V*(trans(V)*Emat);
return LIFT;
}
startUp1d::startUp1d(int N,int K) {
NODETOL=1e-10;
r = JacobiGL(0,0,N);
Np = N+1;
Nfp = 1;
Nfaces =2;
V = Vandermonde1D(N,r);
Dr = Dmatrix1D(N,r,V);
invV = V.inverse();
MatrixXd Emat(Np,Nfaces*Nfp);
Emat.setZero(Np,2);
Emat(0,0)=1.0;
Emat(Np-1,1)=1.0;
LIFT = V*V.transpose()*Emat;
EToV.setZero(K,2);
VX.setZero(K+1);
EToV = meshGen(0.0,1.0,K,Nv,VX);
ArrayXi va,vb;
va = EToV.col(0);
vb=EToV.col(1);
VectorXd v1(K),v2(K);
{ int temp=0;
for(int i=0; i<K; i++)
{ temp = va(i);
v1(i)= VX(temp-1);
temp = vb(i);
v2(i)= VX(temp-1);
}
}
VectorXd temp1;
temp1.setOnes(N+1,1);
x =temp1*v1.transpose()+ 0.5*((r.array()+1).matrix())*(v2-v1).transpose();
J = Dr*x;
rx = 1.0/J.array();
Fmask.setZero(2);
Fmask(0)=0;
Fmask(1)=Np-1;
std::cout<<"Fx"<<Fmask<<"\n";
Fx.setZero(2,K);
Fx.row(0)=x.row(0);
Fx.row(1)=x.row(Np-1);
std::cout<<"Fx"<<Fx<<"\n";
nx=Normals1D(Nfp,Nfaces,K);
Fscale.setZero(2,K);
Fscale.row(0)=J.row(0);
Fscale.row(1)=J.row(Np-1);
Fscale = 1.0/Fscale.array();
EToEF = Connect1DEToE(EToV);
std::cout<<"Fscale "<<"\n"<<Fscale<<"\n";
std::cout<<"Fscale "<<"\n"<<EToEF<<"\n";
}
double omxFreeVar::getCurValue(omxState *os)
{
omxFreeVarLocation &loc = locations[0];
EigenMatrixAdaptor Emat(os->matrixList[loc.matrix]);
return Emat(loc.row, loc.col);
}
