25 #include "reference_element_aux.icc"
45 _nnod_on_subgeo_remainder(),
52 _bkm1_node_internal_d()
70 const Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1>&
73 base::_initialize_data_guard (hat_K);
74 return _hat_node [hat_K.
variant()];
77 const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>&
80 base::_initialize_data_guard (hat_K);
84 const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>&
87 base::_initialize_data_guard (hat_K);
88 return _inv_vdm [hat_K.
variant()];
95 for (
size_type map_d = 0; map_d < 4; ++map_d) {
96 base::_ndof_on_subgeo [map_d].fill (0);
97 base::_nnod_on_subgeo [map_d].fill (0);
114 base::_helper_discontinuous_ndof_on_subgeo_inplace_change (base::is_continuous(), base::_ndof_on_subgeo);
115 base::_helper_initialize_first_ixxx_by_dimension_from_nxxx_on_subgeo (base::_ndof_on_subgeo, base::_first_idof_by_dimension);
125 qopt.set_order (2*(k+2));
138 _nnod_on_subgeo_remainder = base::_nnod_on_subgeo;
139 base::_helper_discontinuous_ndof_on_subgeo_inplace_change (base::is_continuous(), base::_nnod_on_subgeo);
140 base::_helper_initialize_first_ixxx_by_dimension_from_nxxx_on_subgeo (base::_nnod_on_subgeo, base::_first_inod_by_dimension);
157 Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1>& hat_node = _hat_node [hat_K.
variant()];
158 hat_node.resize (base::_first_inod_by_dimension [
variant][
d+1]);
162 for (
size_type loc_isid = 0, loc_nsid = hat_K.
n_subgeo(
d-1); loc_isid < loc_nsid; ++loc_isid) {
166 Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1> hat_node_sid;
168 switch (base::_sopt.get_node()) {
177 error_macro (
"unsupported node set: " << base::_sopt.get_node_name());
179 point loc_vertex [4];
180 for (
size_type loc_jsidvert = 0; loc_jsidvert < loc_nsidvert; ++loc_jsidvert) {
182 loc_vertex[loc_jsidvert] = hat_K.
vertex (loc_jvertex);
184 for (
size_type loc_inod_sid = 0, loc_nnod_sid = hat_node_sid.size(); loc_inod_sid < loc_nnod_sid; ++loc_inod_sid) {
185 check_macro (loc_inod <
size_t(hat_node.size()),
"invalid loc_inod");
186 T xi0 = hat_node_sid [loc_inod_sid][0],
187 xi1 = hat_node_sid [loc_inod_sid][1];
188 if (loc_nsidvert == 4) {
193 hat_node[loc_inod][
alpha] = loc_vertex [0][
alpha];
195 hat_node[loc_inod][
alpha] += xi0*(loc_vertex[1][
alpha] - loc_vertex[0][
alpha]);
198 hat_node[loc_inod][
alpha] += xi1*(loc_vertex[loc_nsidvert-1][
alpha] - loc_vertex[0][
alpha]);
208 Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1> hat_node_internal;
210 switch (base::_sopt.get_node()) {
219 error_macro (
"unsupported node set: " << base::_sopt.get_node_name());
221 trace_macro (
"hat_node_internal.size="<<hat_node_internal.size());
222 for (
size_type loc_inod_int = 0; loc_inod_int <
size_type(hat_node_internal.size()); ++loc_inod_int) {
223 trace_macro (
"hat_node_internal["<<loc_inod_int<<
"]="<<hat_node_internal[loc_inod_int]);
224 hat_node[loc_inod] = hat_node_internal [loc_inod_int];
229 last_q = _quad.end(hat_K); iter_q != last_q; iter_q++) {
230 hat_node[loc_inod] = (*iter_q).x;
235 check_macro (loc_inod == loc_nnod,
"invalid node count: loc_inod="<<loc_inod<<
" and loc_nnod="<<loc_nnod);
245 size_type dim_Pkp1 = _b_pre_kp1.ndof (hat_K);
247 for (
size_type loc_isid = 0, loc_nsid = hat_K.
n_subgeo(
d-1); loc_isid < loc_nsid; ++loc_isid) {
250 loc_ndof_sid_tot += _nnod_on_subgeo_remainder [
d][hat_S.
variant()];
253 size_type loc_nnod_sid_tot = loc_ndof_sid_tot;
257 warning_macro (
"first_inod(hat_K,d) ="<<base::first_inod(hat_K,
d));
258 warning_macro (
"first_inod(hat_K,d+1)="<<base::first_inod(hat_K,
d+1));
264 warning_macro (
"first_idof(hat_K,d-1)="<<base::first_idof(hat_K,
d-1));
265 warning_macro (
"first_idof(hat_K,d) ="<<base::first_idof(hat_K,
d));
266 warning_macro (
"first_idof(hat_K,d+1)="<<base::first_idof(hat_K,
d+1));
269 warning_macro (
"a_tilde(loc_ndof)="<<loc_ndof<<
",d*dim(Pkp1)="<<
d*dim_Pkp1<<
")");
276 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> tilde_a (loc_ndof,
d*dim_Pkp1);
282 trace_macro (
"basis(1): (q,0) and (0,r), q,r in basis(Pk)...");
283 for (
size_type loc_comp_idof = 0; loc_comp_idof < dim_Pk; ++loc_comp_idof) {
287 trace_macro (
"loc_idof="<<loc_idof<<
", loc_jpkp1="<<loc_jpkp1);
288 tilde_a (loc_idof, loc_jpkp1) = 1;
292 trace_macro (
"basis(2): (x0*p,x1*p), p in basis(P_k)\basis(P_{k-1}) [exactly k degree]");
293 std::vector<size_type> inod2ideg_kp1;
294 build_inod2ideg (hat_K, k+1, inod2ideg_kp1);
303 std::vector<point_basic<size_type> > power_index;
304 make_power_indexes_sorted_by_degrees (hat_K, k, power_index);
305 for (
size_type loc_ideg = dim_Pkm1, loc_ndeg = power_index.size(); loc_ideg < loc_ndeg; ++loc_ideg) {
308 size_type loc_idof =
d*dim_Pk + (loc_ideg - dim_Pkm1);
310 size_type loc_inod_kp1 = ilat2loc_inod (hat_K, k+1, ilat);
311 size_type loc_ideg_kp1 = inod2ideg_kp1 [loc_inod_kp1];
313 trace_macro (
"loc_idof="<<loc_idof<<
", loc_jpkp1d="<<loc_jpkp1d);
314 tilde_a (loc_idof, loc_jpkp1d) = 1;
329 std::vector<point_basic<size_type> > power_index_sub;
330 make_power_indexes_sorted_by_degrees (hat_sub, k, power_index_sub);
331 for (
size_type loc_ideg = 0, loc_ndeg = power_index_sub.size(); loc_ideg < loc_ndeg; ++loc_ideg) {
337 ilat [(
alpha+1)%
d] = ilat_sub[0];
338 if (
d == 3) ilat [(
alpha+2)%
d] = ilat_sub[1];
339 size_type loc_inod_kp1 = ilat2loc_inod (hat_K, k+1, ilat);
340 size_type loc_ideg_kp1 = inod2ideg_kp1 [loc_inod_kp1];
342 trace_macro (
"loc_idof="<<loc_idof<<
", loc_jpkp1d="<<loc_jpkp1d);
343 tilde_a (loc_idof, loc_jpkp1d) = 1;
349 default:
error_macro (
"unexpected element `"<<hat_K.
name()<<
"' (HINT: see BerDur-2013)");
351 #undef DEBUG_RTK // print matrix
353 cout << setprecision(std::numeric_limits<T>::digits10)
354 <<
"tilde_a=[" << endl << tilde_a <<
"]"<<endl
355 <<
"[u,s,vt]=svd(tilde_a)" << endl
356 <<
"id=eye(size(s))" << endl
357 <<
"a=u*id*vt" << endl
367 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>
368 u (tilde_a.rows(), tilde_a.rows()),
369 vt (tilde_a.cols(), tilde_a.cols());
370 Eigen::Matrix<T,Eigen::Dynamic,1> s (tilde_a.rows());
371 Eigen::JacobiSVD<Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> >
372 svd (tilde_a, Eigen::ComputeFullU | Eigen::ComputeFullV);
374 s = svd.singularValues();
380 rank_s += (abs(s[loc_idof]) > eps) ? 1 : 0;
383 "invalid polynomial space dimension = " << rank_s <<
" < loc_ndof = " << loc_ndof);
384 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> id (tilde_a.rows(), tilde_a.cols());
386 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>
a =
id*vt.transpose();
389 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> s1 (tilde_a.rows(), tilde_a.cols());
391 for (
size_type iloc = 0; iloc < size_t(tilde_a.rows()); iloc++) {
392 s1(iloc,iloc) = s(iloc);
394 cout <<
"s1 = ["<< endl << s1 <<
"];" << endl
395 <<
"u1 = ["<< endl <<
u <<
"];"<<endl
396 <<
"vt1 = ["<< endl << vt <<
"];"<<endl
397 <<
"id1 = ["<< endl <<
id <<
"];"<<endl
398 <<
"a1 = ["<< endl <<
a <<
"]"<<endl
399 <<
"err=norm(tilde_a-u*s*vt')"<<endl
400 <<
"err1=norm(tilde_a-u1*s1*vt1')"<<endl
401 <<
"err_a=abs(a-a1)"<<endl
402 <<
"err_svd=max(max(abs(a-a1)))"<<endl
403 <<
"err_u=max(max(abs(u-u1)))"<<endl
404 <<
"err_v=max(max(abs(vt-vt1)))"<<endl
405 <<
"err_s=max(diag(s1)-diag(s))"<<endl
407 T err_svd = (tilde_a -
u*s1*vt.transpose()).
norm();
408 cout <<
"err_svd = " << err_svd << endl;
419 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>
421 bkm1_node_internal_d = _bkm1_node_internal_d [
variant];
424 Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1> hat_node_internal (loc_nnod_int);
425 for (
size_type loc_inod_int = 0; loc_inod_int < loc_nnod_int; ++loc_inod_int) {
426 size_type loc_inod = loc_nnod_sid_tot + loc_inod_int;
427 hat_node_internal [loc_inod_int] = hat_node [loc_inod];
429 string basis_dof_name;
430 switch (base::_sopt.get_raw_polynomial()) {
434 default:
error_macro (
"unsupported raw polynomial basis `"<<base::_sopt.get_raw_polynomial_name()<<
"'");
446 bkm1_node_internal_d [
alpha] = bkm1_node_internal_d [0];
454 b_dof_k (basis_dof_name+
itos(k));
455 std::array<Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1>,3> hat_node_internal_comp;
457 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>
459 bkm1_node_internal_comp,
460 bk_node_internal_comp;
463 hat_node_internal_comp [
alpha].resize (hat_node_internal.size());
464 for (
size_type loc_inod_int = 0, loc_nnod_int = hat_node_internal.size(); loc_inod_int < loc_nnod_int; ++loc_inod_int) {
466 hat_node_internal_comp [
alpha][loc_inod_int][0] = (1+hat_node_internal [loc_inod_int][
alpha])/2;
471 size_type loc_ndof_int = bkm1_node_internal_comp[0].cols()*
pow(bk_node_internal_comp[0].cols(),
d-1);
475 bkm1_node_internal_d [
alpha].resize (hat_node_internal.size(), loc_ndof_int);
476 for (
size_type loc_inod_int = 0, loc_nnod_int = hat_node_internal.size(); loc_inod_int < loc_nnod_int; ++loc_inod_int) {
481 bkm1_node_internal_d [
alpha ] (loc_inod_int,loc_idof_int)
482 = bkm1_node_internal_comp [
alpha ] (loc_inod_int,i)
483 * bk_node_internal_comp [alpha2] (loc_inod_int,j);
490 bkm1_node_internal_d [
alpha ] (loc_inod_int,loc_idof_int)
491 = bkm1_node_internal_comp [
alpha ] (loc_inod_int,i)
492 * bk_node_internal_comp [alpha2] (loc_inod_int,j)
493 * bk_node_internal_comp [alpha3] (loc_inod_int,k);
508 size_type loc_n_bkp1 = _b_pre_kp1.ndof (hat_K);
509 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> bkp1_node (loc_nnod, loc_n_bkp1);
513 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> bkp1d_dof (loc_ndof,
d*loc_n_bkp1);
514 bkp1d_dof.fill (std::numeric_limits<T>::max());
515 Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1> bkp1d_j_node (loc_nnod);
516 Eigen::Matrix<T,Eigen::Dynamic,1> bkp1d_j_dof (loc_ndof);
517 for (
size_type loc_j_bkp1 = 0; loc_j_bkp1 < loc_n_bkp1; ++loc_j_bkp1) {
519 for (
size_type loc_inod = 0; loc_inod < loc_nnod; ++loc_inod) {
521 bkp1d_j_node [loc_inod][
alpha] = bkp1_node(loc_inod,loc_j_bkp1);
523 bkp1d_j_dof.fill (std::numeric_limits<T>::max());
524 _compute_dofs (hat_K, bkp1d_j_node, bkp1d_j_dof);
526 check_macro (bkp1d_dof.rows() == bkp1d_j_dof.size(),
"invalid sizes");
527 bkp1d_dof.col (loc_j_bkp1d) = bkp1d_j_dof;
536 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>& vdm = _vdm [hat_K.
variant()];
537 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>& inv_vdm = _inv_vdm[hat_K.
variant()];
538 vdm = bkp1d_dof*
a.transpose();
539 bool invert_ok =
invert(vdm, inv_vdm);
546 "unisolvence failed for " <<
base::name() <<
"(" << hat_K.
name() <<
") basis");
550 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>& bar_a = _bar_a [hat_K.
variant()];
551 bar_a = inv_vdm.transpose()*
a;
553 cout <<
"bkp1d_dof=[" << endl << bkp1d_dof <<
"]"<<endl
554 <<
"vdm=[" << endl << vdm <<
"]"<<endl
555 <<
"det_vdm=" << vdm.determinant() <<endl
556 <<
"cond_vdm=" <<
cond(vdm) <<endl
557 <<
"bar_a1=inv(vdm)'*a;"<<endl
558 <<
"bar_a=[" << endl << bar_a <<
"]"<<endl;
569 Eigen::Matrix<value_type,Eigen::Dynamic,1>&
value)
const
571 base::_initialize_data_guard (hat_K);
577 const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>& bar_a = _bar_a [hat_K.
variant()];
578 Eigen::Matrix<T,Eigen::Dynamic,1> bkp1;
579 _b_pre_kp1.evaluate (hat_K, hat_x, bkp1);
580 value.resize (loc_ndof);
591 for (
size_type loc_idof = 0; loc_idof < loc_ndof; ++loc_idof) {
593 for (
size_type loc_jdof_bkp1 = 0, loc_ndof_bkp1 = bkp1.size(); loc_jdof_bkp1 < loc_ndof_bkp1; ++loc_jdof_bkp1) {
596 value[loc_idof][
alpha] += bar_a(loc_idof,loc_jdof_bkp1d)*bkp1[loc_jdof_bkp1];
608 base::_initialize_data_guard (hat_K);
614 const Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>& bar_a = _bar_a [hat_K.
variant()];
615 Eigen::Matrix<point_basic<T>,Eigen::Dynamic,1> grad_bkp1;
616 _b_pre_kp1.grad_evaluate (hat_K, hat_x, grad_bkp1);
617 value.resize (loc_ndof);
629 for (
size_type loc_idof = 0; loc_idof < loc_ndof; ++loc_idof) {
631 for (
size_type loc_jdof_bkp1 = 0, loc_ndof_bkp1 = grad_bkp1.size(); loc_jdof_bkp1 < loc_ndof_bkp1; ++loc_jdof_bkp1) {
635 value[loc_idof](
alpha,
beta) += bar_a(loc_idof,loc_jdof_bkp1d)*grad_bkp1[loc_jdof_bkp1][
beta];
657 const Eigen::Matrix<value_type,Eigen::Dynamic,1>& f_xnod,
658 Eigen::Matrix<T,Eigen::Dynamic,1>& dof)
const
661 base::_initialize_data_guard (hat_K);
666 dof.resize (loc_ndof);
672 for (
size_type loc_isid = 0, loc_nsid = hat_K.
n_subgeo(
d-1); loc_isid < loc_nsid; ++loc_isid) {
678 for (
size_type loc_idof_sid = 0; loc_idof_sid < loc_ndof_sid; ++loc_idof_sid) {
679 dof[loc_idof] = hat_S_meas*
dot(f_xnod[loc_inod],hat_n);
687 Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic>
689 bkm1_node_internal_d = _bkm1_node_internal_d [hat_K.
variant()];
692 size_type loc_ndof_int_d =
d*bkm1_node_internal_d[0].cols();
694 check_macro (loc_ndof == loc_ndof_boundary + loc_ndof_int_d,
695 "invalid internal dof count: loc_ndof="<<loc_ndof
696 <<
", loc_ndof_boundary="<<loc_ndof_boundary
697 <<
", loc_ndof_int_d="<<loc_ndof_int_d);
702 for (
size_type loc_idof_int = 0, loc_ndof_int = bkm1_node_internal_d[0].cols(); loc_idof_int < loc_ndof_int; ++loc_idof_int) {
703 size_type loc_inod = first_loc_inod_int + loc_idof_int;
705 dof [loc_idof] = f_xnod [loc_inod][
alpha];
710 for (
size_type loc_idof_int = 0, loc_ndof_int = bkm1_node_internal_d[0].cols(); loc_idof_int < loc_ndof_int; ++loc_idof_int) {
712 loc_inod = first_loc_inod_int;
716 last_q = _quad.end(hat_K); iter_q != last_q; iter_q++, inod_q++, ++loc_inod) {
717 sum += f_xnod [loc_inod][
alpha]
718 *bkm1_node_internal_d[
alpha] (inod_q, loc_idof_int)
722 dof [loc_idof] = sum;
727 check_macro (loc_idof == loc_ndof,
"invalid dof count");
733 #define _RHEOLEF_instanciation(T) \
734 template class basis_fem_RTk<T>;