static void exact_sol(double x, double y, scalar& u0, scalar& u1, scalar& u1dx, scalar& u0dy)
{
scalar dx,dy;
u0 = exact0(x,y,dx,dy);
u1 = exact1(x,y,dx,dy);
scalar Hr = der_Hr(x,y);
scalar Ht = der_Ht(x,y);
scalar Hrr = der_Hrr(x,y);
scalar Hrt = der_Hrt(x,y);
scalar Htr = der_Htr(x,y);
scalar Htt = der_Htt(x,y);
double r = sqrt(x*x + y*y);
double theta = atan2(y,x);
scalar i = cplx(0.0,1.0);
u1dx = i * (( Hrr * x/r + Hrt * (-y/(r*r))) * x/r + Hr * (y*y)/(r*r*r) -
((Htr * x/r + Htt * (-y/(r*r))) * y/(r*r) + Ht * (-2.0*x*y/(r*r*r*r))));
u0dy = -i * (( Hrr * y/r + Hrt * x/(r*r)) * y/r + Hr * (x*x)/(r*r*r) +
(Htr * y/r + Htt * x/(r*r)) * x/(r*r) + Ht * (-2.0*x*y/(r*r*r*r)));
}
cplx bc_values(int marker, double x, double y)
{
scalar dx, dy;
return exact0(x, y, dx, dy)*tau[marker][0] + exact1(x, y, dx, dy)*tau[marker][1];
}