Scalar jac(int n, double *wt, Func<Real> *u, Func<Real> *v, Geom<Real> *e, ExtData<Scalar> *ext)
{
Scalar result = 0;
Func<Scalar>* u_prev = ext->fn[0];
for (int i = 0; i < n; i++)
result += wt[i] * (dlam_du(u_prev->val[i]) * u->val[i] * (u_prev->dx[i] * v->dx[i] + u_prev->dy[i] * v->dy[i])
+ lam(u_prev->val[i]) * (u->dx[i] * v->dx[i] + u->dy[i] * v->dy[i]));
return result;
}
Scalar J_cranic(int n, double *wt, Func<Real> *u_ext[], Func<Real> *u, Func<Real> *v, Geom<Real> *e, ExtData<Scalar> *ext)
{
Scalar result = 0;
Func<Scalar>* u_prev_newton = u_ext[0];
for (int i = 0; i < n; i++)
result += wt[i] * (u->val[i] * v->val[i] / TAU +
0.5 * dlam_du(u_prev_newton->val[i]) * u->val[i] * (u_prev_newton->dx[i] * v->dx[i] + u_prev_newton->dy[i] * v->dy[i])
+ 0.5 * lam(u_prev_newton->val[i]) * (u->dx[i] * v->dx[i] + u->dy[i] * v->dy[i]));
return result;
}
Scalar jac2(int n, double *wt, Func<Real> *u_ext[], Func<Real> *u, Func<Real> *v, Geom<Real> *e, ExtData<Scalar> *ext)
{
Scalar result = 0;
Func<Scalar>* Y2_prev_newton = u_ext[0];
for (int i = 0; i < n; i++)
result += wt[i] * (u->val[i] * v->val[i]
+ GAMMA * TAU * (dlam_du(Y2_prev_newton->val[i]) * u->val[i] * (Y2_prev_newton->dx[i] * v->dx[i]
+ Y2_prev_newton->dy[i] * v->dy[i])
+ lam(Y2_prev_newton->val[i]) * (u->dx[i] * v->dx[i]
+ u->dy[i] * v->dy[i])));
return result;
}
Scalar jac_sdirk(int n, double *wt, Func<Real> *u_ext[], Func<Real> *u, Func<Real> *v,
Geom<Real> *e, ExtData<Scalar> *ext)
{
Scalar result = 0;
Func<Scalar>* u_prev_newton = u_ext[0];
for (int i = 0; i < n; i++)
result += wt[i] * (u->val[i] * v->val[i] / TAU
+ BUTCHER_A_11 * (dlam_du(u_prev_newton->val[i]) * u->val[i]
* (u_prev_newton->dx[i] * v->dx[i] + u_prev_newton->dy[i] * v->dy[i])
+ lam(u_prev_newton->val[i]) * (u->dx[i] * v->dx[i] + u->dy[i] * v->dy[i])));
return result;
}
Scalar stac_jacobian(int n, double *wt, Func<Real> *u_ext[], Func<Real> *u, Func<Real> *v,
Geom<Real> *e, ExtData<Scalar> *ext)
{
Func<Scalar>* u_prev = u_ext[0];
// This is a temporary workaround. The stage time t_n + h * c_i
// can be accessed via u_stage_time->val[0];
// In this particular case the stage time is not needed as
// the form does not depend explicitly on time.
Func<Scalar>* u_stage_time = ext->fn[0];
// Stationary part of the Jacobian matrix (time derivative term left out).
Scalar result1 = 0, result2 = 0;
for (int i = 0; i < n; i++) {
result1 += -wt[i] * dlam_du(u_prev->val[i]) * u->val[i] * (u_prev->dx[i] * v->dx[i] + u_prev->dy[i] * v->dy[i]);
result2 += -wt[i] * lam(u_prev->val[i]) * (u->dx[i] * v->dx[i] + u->dy[i] * v->dy[i]);
}
return result1 + result2;
}