Scalar res(int n, double *wt, 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] * (lam(u_prev->val[i]) * (u_prev->dx[i] * v->dx[i] + u_prev->dy[i] * v->dy[i])
- heat_src(e->x[i], e->y[i]) * v->val[i]);
return result;
}
Scalar res_ss(int n, double *wt, Func<Real> *u_ext[], Func<Real> *v, Geom<Real> *e, ExtData<Scalar> *ext, double t)
{
Scalar result = 0;
Func<Scalar>* Y_prev_newton = u_ext[0];
for (int i = 0; i < n; i++) {
result += wt[i] * (lam(Y_prev_newton->val[i]) * (Y_prev_newton->dx[i] * v->dx[i] + Y_prev_newton->dy[i] * v->dy[i])
- heat_src(e->x[i], e->y[i], t) * v->val[i]);
}
return result;
}
Scalar F_euler(int n, double *wt, Func<Real> *u_ext[], Func<Real> *v, Geom<Real> *e, ExtData<Scalar> *ext)
{
Scalar result = 0;
Func<Scalar>* u_prev_newton = u_ext[0];
Func<Scalar>* u_prev_time = ext->fn[0];
for (int i = 0; i < n; i++)
result += wt[i] * ((u_prev_newton->val[i] - u_prev_time->val[i]) * v->val[i] / TAU +
lam(u_prev_newton->val[i]) * (u_prev_newton->dx[i] * v->dx[i] + u_prev_newton->dy[i] * v->dy[i])
- heat_src(e->x[i], e->y[i]) * v->val[i]);
return result;
}
Scalar res1(int n, double *wt, Func<Real> *u_ext[], Func<Real> *v, Geom<Real> *e, ExtData<Scalar> *ext)
{
Scalar result = 0;
Func<Scalar>* Y1_prev_newton = u_ext[0];
Func<Scalar>* u_prev_time = ext->fn[0];
for (int i = 0; i < n; i++)
result += wt[i] * ((Y1_prev_newton->val[i] - u_prev_time->val[i]) * v->val[i]
+ GAMMA * TAU * (lam(Y1_prev_newton->val[i]) * (Y1_prev_newton->dx[i] * v->dx[i]
+ Y1_prev_newton->dy[i] * v->dy[i])
- heat_src(e->x[i], e->y[i], TIME+GAMMA*TAU) * v->val[i]));
return result;
}
Scalar stac_residual(int n, double *wt, Func<Real> *u_ext[], 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 residual (time derivative term left out).
Scalar result1 = 0, result2 = 0;
for (int i = 0; i < n; i++) {
result1 = result1 - wt[i] * lam(u_prev->val[i]) * (u_prev->dx[i] * v->dx[i] + u_prev->dy[i] * v->dy[i]);
result2 = result2 + wt[i] * heat_src(e->x[i], e->y[i]) * v->val[i];
}
return result1 + result2;
}