// Actual evaluation of volume matrix form (calculates integral)
scalar FeProblem::eval_form(WeakForm::MatrixFormVol *mfv, Tuple<Solution *> u_ext, PrecalcShapeset *fu, PrecalcShapeset *fv, RefMap *ru, RefMap *rv)
{
// determine the integration order
int inc = (fu->get_num_components() == 2) ? 1 : 0;
AUTOLA_OR(Func<Ord>*, oi, wf->neq);
for (int i = 0; i < wf->neq; i++) oi[i] = init_fn_ord(u_ext[i]->get_fn_order() + inc);
Func<Ord>* ou = init_fn_ord(fu->get_fn_order() + inc);
Func<Ord>* ov = init_fn_ord(fv->get_fn_order() + inc);
ExtData<Ord>* fake_ext = init_ext_fns_ord(mfv->ext);
double fake_wt = 1.0;
Geom<Ord>* fake_e = init_geom_ord();
Ord o = mfv->ord(1, &fake_wt, oi, ou, ov, fake_e, fake_ext);
int order = ru->get_inv_ref_order();
order += o.get_order();
limit_order_nowarn(order);
for (int i = 0; i < wf->neq; i++) { oi[i]->free_ord(); delete oi[i]; }
ou->free_ord(); delete ou;
ov->free_ord(); delete ov;
delete fake_e;
fake_ext->free_ord(); delete fake_ext;
// eval the form
Quad2D* quad = fu->get_quad_2d();
double3* pt = quad->get_points(order);
int np = quad->get_num_points(order);
// init geometry and jacobian*weights
if (cache_e[order] == NULL)
{
cache_e[order] = init_geom_vol(ru, order);
double* jac = ru->get_jacobian(order);
cache_jwt[order] = new double[np];
for(int i = 0; i < np; i++)
cache_jwt[order][i] = pt[i][2] * jac[i];
}
Geom<double>* e = cache_e[order];
double* jwt = cache_jwt[order];
// function values and values of external functions
AUTOLA_OR(Func<scalar>*, prev, wf->neq);
for (int i = 0; i < wf->neq; i++) prev[i] = init_fn(u_ext[i], rv, order);
Func<double>* u = get_fn(fu, ru, order);
Func<double>* v = get_fn(fv, rv, order);
ExtData<scalar>* ext = init_ext_fns(mfv->ext, rv, order);
scalar res = mfv->fn(np, jwt, prev, u, v, e, ext);
for (int i = 0; i < wf->neq; i++) { prev[i]->free_fn(); delete prev[i]; }
ext->free(); delete ext;
return res;
}
// function used to calculate L2 norm of the solution
double norm_fn_l2_axisym(MeshFunction* sln, RefMap* ru)
{
Quad2D* quad = sln->get_quad_2d();
int o = 2 *sln->get_fn_order() + ru->get_inv_ref_order();
limit_order_nowarn(o);
sln->set_quad_order(o, H2D_FN_VAL);
scalar* uval = sln->get_fn_values();
double* x = ru->get_phys_x(o);
double result = 0.0;
h1_integrate_expression(x[i]*sqr(uval[i]));
return 2*M_PI*result;
}
double KellyTypeAdapt::eval_solution_norm(Adapt::MatrixFormVolError* form, RefMap *rm, MeshFunction* sln)
{
// determine the integration order
int inc = (sln->get_num_components() == 2) ? 1 : 0;
Func<Ord>* ou = init_fn_ord(sln->get_fn_order() + inc);
double fake_wt = 1.0;
Geom<Ord>* fake_e = init_geom_ord();
Ord o = form->ord(1, &fake_wt, NULL, ou, ou, fake_e, NULL);
int order = rm->get_inv_ref_order();
order += o.get_order();
Solution *sol = static_cast<Solution *>(sln);
if(sol && sol->get_type() == HERMES_EXACT) {
limit_order_nowarn(order);
}
else {
limit_order(order);
}
ou->free_ord(); delete ou;
delete fake_e;
// eval the form
Quad2D* quad = sln->get_quad_2d();
double3* pt = quad->get_points(order);
int np = quad->get_num_points(order);
// init geometry and jacobian*weights
Geom<double>* e = init_geom_vol(rm, order);
double* jac = rm->get_jacobian(order);
double* jwt = new double[np];
for(int i = 0; i < np; i++)
jwt[i] = pt[i][2] * jac[i];
// function values
Func<scalar>* u = init_fn(sln, order);
scalar res = form->value(np, jwt, NULL, u, u, e, NULL);
e->free(); delete e;
delete [] jwt;
u->free_fn(); delete u;
return std::abs(res);
}
// Function used to calculate H1 norm of the solution.
double norm_fn_h1_axisym(MeshFunction* sln, RefMap* ru)
{
Quad2D* quad = sln->get_quad_2d();
int o = 2 * sln->get_fn_order() + ru->get_inv_ref_order();
limit_order_nowarn(o);
sln->set_quad_order(o);
scalar *uval, *dudx, *dudy;
uval = sln->get_fn_values();
sln->get_dx_dy_values(dudx, dudy);
double* x = ru->get_phys_x(o);
double result = 0.0;
h1_integrate_expression(x[i] * (sqr(uval[i]) + sqr(dudx[i]) + sqr(dudy[i])) );
return 2*M_PI*result;
}
// function used to calculate error in L2 norm
double error_fn_l2_axisym(MeshFunction* sln1, MeshFunction* sln2, RefMap* ru, RefMap* rv)
{
Quad2D* quad = sln1->get_quad_2d();
int o = 2*std::max(sln1->get_fn_order(), sln2->get_fn_order()) + ru->get_inv_ref_order();
limit_order_nowarn(o);
sln1->set_quad_order(o, H2D_FN_VAL);
sln2->set_quad_order(o, H2D_FN_VAL);
scalar *uval, *vval;
uval = sln1->get_fn_values();
vval = sln2->get_fn_values();
double* x = ru->get_phys_x(o);
double result = 0.0;
h1_integrate_expression(x[i]*sqr(uval[i] - vval[i]));
return 2*M_PI*result;
}
// Function used to calculate error in H1 norm.
double error_fn_h1_axisym(MeshFunction* sln1, MeshFunction* sln2, RefMap* ru, RefMap* rv)
{
Quad2D* quad = sln1->get_quad_2d();
int o = 2*std::max(sln1->get_fn_order(), sln2->get_fn_order()) + ru->get_inv_ref_order();
limit_order_nowarn(o);
sln1->set_quad_order(o);
sln2->set_quad_order(o);
scalar *uval, *vval, *dudx, *dudy, *dvdx, *dvdy;
uval = sln1->get_fn_values();
vval = sln2->get_fn_values();
sln1->get_dx_dy_values(dudx, dudy);
sln2->get_dx_dy_values(dvdx, dvdy);
double* x = ru->get_phys_x(o);
double result = 0.0;
h1_integrate_expression(x[i] * (sqr(uval[i] - vval[i]) +
sqr(dudx[i] - dvdx[i]) + sqr(dudy[i] - dvdy[i])) );
return 2*M_PI*result;
}