Line data Source code
1 : // The libMesh Finite Element Library.
2 : // Copyright (C) 2002-2025 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
3 :
4 : // This library is free software; you can redistribute it and/or
5 : // modify it under the terms of the GNU Lesser General Public
6 : // License as published by the Free Software Foundation; either
7 : // version 2.1 of the License, or (at your option) any later version.
8 :
9 : // This library is distributed in the hope that it will be useful,
10 : // but WITHOUT ANY WARRANTY; without even the implied warranty of
11 : // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 : // Lesser General Public License for more details.
13 :
14 : // You should have received a copy of the GNU Lesser General Public
15 : // License along with this library; if not, write to the Free Software
16 : // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17 :
18 : #include "libmesh/variational_smoother_system.h"
19 :
20 : #include "libmesh/elem.h"
21 : #include "libmesh/face_tri3.h"
22 : #include "libmesh/face_tri6.h"
23 : #include "libmesh/fe_base.h"
24 : #include "libmesh/fe_interface.h"
25 : #include "libmesh/fem_context.h"
26 : #include "libmesh/mesh.h"
27 : #include "libmesh/numeric_vector.h"
28 : #include "libmesh/parallel_ghost_sync.h"
29 : #include "libmesh/quadrature.h"
30 : #include "libmesh/string_to_enum.h"
31 : #include "libmesh/utility.h"
32 : #include "libmesh/enum_to_string.h"
33 : #include <libmesh/reference_elem.h>
34 :
35 : // C++ includes
36 : #include <functional> // std::reference_wrapper
37 :
38 : namespace libMesh
39 : {
40 :
41 : /*
42 : * Gets the dof_id_type value corresponding to the minimum of the Real value.
43 : */
44 152480 : void communicate_pair_min(std::pair<Real, dof_id_type> & pair, const Parallel::Communicator & comm)
45 : {
46 : // Get rank where minimum occurs
47 : unsigned int rank;
48 152480 : comm.minloc(pair.first, rank);
49 152480 : comm.broadcast(pair.second, rank);
50 152480 : }
51 :
52 : /*
53 : * Gets the dof_id_type value corresponding to the maximum of the Real value.
54 : */
55 152480 : void communicate_pair_max(std::pair<Real, dof_id_type> & pair, const Parallel::Communicator & comm)
56 : {
57 : // Get rank where minimum occurs
58 : unsigned int rank;
59 152480 : comm.maxloc(pair.first, rank);
60 152480 : comm.broadcast(pair.second, rank);
61 152480 : }
62 :
63 : /**
64 : * Function to prevent dividing by zero for degenerate elements
65 : */
66 6783840 : Real chi_epsilon(const Real & x, const Real epsilon_squared)
67 : {
68 7348968 : return 0.5 * (x + std::sqrt(epsilon_squared + Utility::pow<2>(x)));
69 : }
70 :
71 : /**
72 : * Given an fe_map, element dimension, and quadrature point index, returns the
73 : * Jacobian of the physical-to-reference mapping.
74 : */
75 6795067 : RealTensor get_jacobian_at_qp(const FEMap & fe_map,
76 : const unsigned int & dim,
77 : const unsigned int & qp)
78 : {
79 6795067 : const auto & dxyzdxi = fe_map.get_dxyzdxi()[qp];
80 1131076 : const auto & dxyzdeta = fe_map.get_dxyzdeta()[qp];
81 1131076 : const auto & dxyzdzeta = fe_map.get_dxyzdzeta()[qp];
82 :
83 : // RealTensors are always 3x3, so we will fill any dimensions above dim
84 : // with 1s on the diagonal. This indicates a 1 to 1 relationship between
85 : // the physical and reference elements in these extra dimensions.
86 6795067 : switch (dim)
87 : {
88 6528 : case 1:
89 : return RealTensor(
90 : dxyzdxi(0), 0, 0,
91 : 0, 1, 0,
92 : 0, 0, 1
93 544 : );
94 : break;
95 :
96 428905 : case 2:
97 : return RealTensor(
98 : dxyzdxi(0), dxyzdeta(0), 0,
99 : dxyzdxi(1), dxyzdeta(1), 0,
100 : 0, 0, 1
101 35502 : );
102 : break;
103 :
104 6359634 : case 3:
105 1058984 : return RealTensor(
106 : dxyzdxi,
107 : dxyzdeta,
108 : dxyzdzeta
109 529492 : ).transpose(); // Note the transposition!
110 : break;
111 :
112 0 : default:
113 0 : libmesh_error_msg("Unsupported dimension.");
114 : }
115 : }
116 :
117 : /**
118 : * Compute the trace of a dim-dimensional matrix.
119 : */
120 6783840 : Real trace(const RealTensor & A, const unsigned int & dim)
121 : {
122 565128 : Real tr = 0.0;
123 26694336 : for (const auto i : make_range(dim))
124 19910496 : tr += A(i, i);
125 :
126 6783840 : return tr;
127 : }
128 :
129 3819 : VariationalSmootherSystem::~VariationalSmootherSystem () = default;
130 :
131 35280 : void VariationalSmootherSystem::assembly (bool get_residual,
132 : bool get_jacobian,
133 : bool apply_heterogeneous_constraints,
134 : bool apply_no_constraints)
135 : {
136 : // Update the mesh based on the current variable values
137 1976 : auto & mesh = this->get_mesh();
138 35280 : this->solution->close();
139 :
140 904052 : for (auto * node : mesh.local_node_ptr_range())
141 : {
142 1757910 : for (const auto d : make_range(mesh.mesh_dimension()))
143 : {
144 1302780 : const auto dof_id = node->dof_number(this->number(), d, 0);
145 : // Update mesh
146 1302780 : (*node)(d) = libmesh_real((*current_local_solution)(dof_id));
147 : }
148 33304 : }
149 :
150 35280 : SyncNodalPositions sync_object(mesh);
151 69572 : Parallel::sync_dofobject_data_by_id (mesh.comm(), mesh.nodes_begin(), mesh.nodes_end(), sync_object);
152 :
153 : // Compute and update mesh quality information
154 35280 : compute_mesh_quality_info();
155 35280 : const bool is_tangled = _mesh_info.mesh_is_tangled;
156 :
157 : // Update _epsilon_squared_assembly based on whether we are untangling or
158 : // smoothing
159 35280 : if (_untangling_solve)
160 : {
161 172 : const Real & min_S = _mesh_info.min_qp_det_S;
162 : // This component is based on what Larisa did in the original code.
163 6312 : const Real variable_component = 100. * Utility::pow<2>(_ref_vol * min_S);
164 6312 : _epsilon_squared_assembly = _epsilon_squared + variable_component;
165 : }
166 :
167 : else
168 28968 : _epsilon_squared_assembly = 0.;
169 :
170 35280 : FEMSystem::assembly(get_residual, get_jacobian, apply_heterogeneous_constraints, apply_no_constraints);
171 :
172 35280 : if (_untangling_solve && !is_tangled)
173 : {
174 : // Mesh is untangled, artificially reduce residual by factor 0.9 to tell
175 : // the solver we are on the right track. The mesh may become re-tangled in
176 : // subsequent nonlinear and line search iterations, so we will not use
177 : // this reduction factor in the case of re-tangulation. This approach
178 : // should drive the solver to eventually favor untangled solutions.
179 4466 : rhs->close();
180 4466 : (*rhs) *= 0.9;
181 : }
182 35280 : }
183 :
184 1349 : void VariationalSmootherSystem::solve()
185 : {
186 1349 : const auto & mesh_info = get_mesh_info();
187 1349 : if (mesh_info.mesh_is_tangled)
188 : {
189 : // Untangling solve
190 142 : _untangling_solve = true;
191 :
192 : // Untangling seems to work better using only the distortion metric.
193 : // For a mixed metric, I've seen it *technically* untangle a mesh to a
194 : // still-suboptimal mesh (i.e., a local minima), but not been able to
195 : // smooth it well because the smoothest solution is on the other side of
196 : // a tangulation barrier.
197 142 : const auto dilation_weight = _dilation_weight;
198 142 : _dilation_weight = 0.;
199 :
200 142 : FEMSystem::solve();
201 :
202 : // Reset the dilation weight
203 142 : _dilation_weight = dilation_weight;
204 : }
205 :
206 : // Smoothing solve
207 1349 : _untangling_solve = false;
208 1349 : FEMSystem::solve();
209 1349 : libmesh_error_msg_if(get_mesh_info().mesh_is_tangled, "The smoothing solve tangled the mesh!");
210 1349 : }
211 :
212 1349 : void VariationalSmootherSystem::init_data ()
213 : {
214 76 : auto & mesh = this->get_mesh();
215 38 : const auto & elem_orders = mesh.elem_default_orders();
216 1349 : libmesh_error_msg_if(elem_orders.size() != 1,
217 : "The variational smoother cannot be used for mixed-order meshes!");
218 1349 : const auto fe_order = *elem_orders.begin();
219 : // Add a variable for each dimension of the mesh
220 : // "r0" for x, "r1" for y, "r2" for z
221 4544 : for (const auto & d : make_range(mesh.mesh_dimension()))
222 6300 : this->add_variable ("r" + std::to_string(d), fe_order);
223 :
224 : // Do the parent's initialization after variables are defined
225 1349 : FEMSystem::init_data();
226 :
227 : // Set the current_local_solution to the current mesh for the initial guess
228 1349 : this->solution->close();
229 :
230 32822 : for (auto * node : mesh.local_node_ptr_range())
231 : {
232 63648 : for (const auto d : make_range(mesh.mesh_dimension()))
233 : {
234 47196 : const auto dof_id = node->dof_number(this->number(), d, 0);
235 : // Update solution
236 47196 : (*solution).set(dof_id, (*node)(d));
237 : }
238 1273 : }
239 :
240 1349 : this->prepare_for_smoothing();
241 1349 : }
242 :
243 1349 : void VariationalSmootherSystem::prepare_for_smoothing()
244 : {
245 : // If this method has already been called to set _ref_vol, just return.
246 1387 : if (std::abs(_ref_vol) > TOLERANCE * TOLERANCE)
247 0 : return;
248 :
249 1349 : std::unique_ptr<DiffContext> con = this->build_context();
250 38 : FEMContext & femcontext = cast_ref<FEMContext &>(*con);
251 1349 : this->init_context(femcontext);
252 :
253 76 : const auto & mesh = this->get_mesh();
254 :
255 1349 : Real elem_averaged_det_S_sum = 0.;
256 :
257 : // Make pre-requests before reinit() for efficiency in
258 : // --enable-deprecated builds, and to avoid errors in
259 : // --disable-deprecated builds.
260 38 : const auto & fe_map = femcontext.get_element_fe(0)->get_fe_map();
261 38 : const auto & JxW = fe_map.get_JxW();
262 :
263 11252 : for (const auto * elem : mesh.active_local_element_ptr_range())
264 : {
265 8592 : femcontext.pre_fe_reinit(*this, elem);
266 8592 : femcontext.elem_fe_reinit();
267 :
268 : // Add target element info, if applicable
269 9308 : if (_target_jacobians.find(elem->type()) == _target_jacobians.end())
270 : {
271 1036 : const auto [target_elem, target_nodes] = get_target_elem(elem->type());
272 1036 : get_target_to_reference_jacobian(target_elem.get(),
273 : femcontext,
274 1036 : _target_jacobians[elem->type()],
275 2072 : _target_jacobian_dets[elem->type()]);
276 : }// if find == end()
277 :
278 : // Reference volume computation
279 716 : Real elem_integrated_det_S = 0.;
280 108576 : for (const auto qp : index_range(JxW))
281 108316 : elem_integrated_det_S += JxW[qp] * _target_jacobian_dets[elem->type()][qp];
282 8592 : const auto ref_elem_vol = elem->reference_elem()->volume();
283 8592 : elem_averaged_det_S_sum += elem_integrated_det_S / ref_elem_vol;
284 :
285 1273 : } // for elem
286 :
287 : // Get contributions from elements on other processors
288 1349 : mesh.comm().sum(elem_averaged_det_S_sum);
289 :
290 1349 : _ref_vol = elem_averaged_det_S_sum / mesh.n_active_elem();
291 1273 : }
292 :
293 77557 : void VariationalSmootherSystem::init_context(DiffContext & context)
294 : {
295 3030 : FEMContext & c = cast_ref<FEMContext &>(context);
296 :
297 3030 : FEBase * my_fe = nullptr;
298 :
299 : // Now make sure we have requested all the data
300 : // we need to build the system.
301 :
302 : // We might have a multi-dimensional mesh
303 : const std::set<unsigned char> & elem_dims =
304 3030 : c.elem_dimensions();
305 :
306 155114 : for (const auto & dim : elem_dims)
307 : {
308 77557 : c.get_element_fe( 0, my_fe, dim );
309 3030 : my_fe->get_nothing();
310 :
311 3030 : auto & fe_map = my_fe->get_fe_map();
312 3030 : fe_map.get_dxyzdxi();
313 3030 : fe_map.get_dxyzdeta();
314 3030 : fe_map.get_dxyzdzeta();
315 3030 : fe_map.get_JxW();
316 :
317 : // Mesh may be tangled, allow negative Jacobians
318 3030 : fe_map.set_jacobian_tolerance(std::numeric_limits<Real>::lowest());
319 :
320 77557 : c.get_side_fe( 0, my_fe, dim );
321 3030 : my_fe->get_nothing();
322 : }
323 :
324 77557 : FEMSystem::init_context(context);
325 77557 : }
326 :
327 :
328 279360 : bool VariationalSmootherSystem::element_time_derivative (bool request_jacobian,
329 : DiffContext & context)
330 : {
331 23256 : FEMContext & c = cast_ref<FEMContext &>(context);
332 :
333 46512 : const Elem & elem = c.get_elem();
334 :
335 279360 : unsigned int dim = c.get_dim();
336 :
337 23256 : unsigned int x_var = 0, y_var = 1, z_var = 2;
338 : // In the case of lower dimensions, we will not access z (1D/2D) or y (1D)
339 279360 : if (dim < 3)
340 : {
341 4148 : z_var = 0;
342 50064 : if (dim < 2)
343 100 : y_var = 0;
344 : }
345 :
346 : // The subvectors and submatrices we need to fill:
347 : // system residual
348 : std::reference_wrapper<DenseSubVector<Number>> F[3] =
349 : {
350 : c.get_elem_residual(x_var),
351 : c.get_elem_residual(y_var),
352 : c.get_elem_residual(z_var)
353 23256 : };
354 : // system jacobian
355 : std::reference_wrapper<DenseSubMatrix<Number>> K[3][3] =
356 : {
357 : {c.get_elem_jacobian(x_var, x_var), c.get_elem_jacobian(x_var, y_var), c.get_elem_jacobian(x_var, z_var)},
358 : {c.get_elem_jacobian(y_var, x_var), c.get_elem_jacobian(y_var, y_var), c.get_elem_jacobian(y_var, z_var)},
359 : {c.get_elem_jacobian(z_var, x_var), c.get_elem_jacobian(z_var, y_var), c.get_elem_jacobian(z_var, z_var)}
360 23256 : };
361 :
362 : // Quadrature info
363 279360 : const auto quad_weights = c.get_element_qrule().get_weights();
364 :
365 279360 : const auto distortion_weight = 1. - _dilation_weight;
366 :
367 : // Get some references to cell-specific data that
368 : // will be used to assemble the linear system.
369 :
370 23256 : const auto & fe_map = c.get_element_fe(0)->get_fe_map();
371 :
372 23256 : const auto & dphidxi_map = fe_map.get_dphidxi_map();
373 23256 : const auto & dphideta_map = fe_map.get_dphideta_map();
374 23256 : const auto & dphidzeta_map = fe_map.get_dphidzeta_map();
375 :
376 : // Integrate the distortion-dilation metric over the reference element
377 3569616 : for (const auto qp : index_range(quad_weights))
378 : {
379 : // Compute quantities needed to evaluate the distortion-dilation metric
380 : // and its gradient and Hessian.
381 : // The metric will be minimized when it's gradient with respect to the node
382 : // locations (R) is zero. For Newton's method, minimizing the gradient
383 : // requires computation of the gradient's Jacobian with respect to R.
384 : // The Jacobian of the distortion-dilation metric's gradientis the Hessian
385 : // of the metric.
386 : //
387 : // Note that the term "Jacobian" has two meanings in this mesh smoothing
388 : // application. The first meaning refers to the Jacobian w.r.t R of the
389 : // gradient w.r.t. R, (i.e., the Hessian of the metric). This is the K
390 : // variable defined above. This is also the Jacobian the 'request_jacobian'
391 : // variable refers to. The second mesning refers to the Jacobian of the
392 : // physical-to-reference element mapping. This is the Jacobian used to
393 : // compute the distorion-dilation metric.
394 : //
395 : // Grab the physical-to-reference mapping Jacobian matrix (i.e., "S") at this qp
396 3564348 : RealTensor S = get_jacobian_at_qp(fe_map, dim, qp);
397 :
398 : // Apply target element transformation
399 3290256 : S *= _target_jacobians[elem.type()][qp];
400 :
401 : // Compute quantities needed for the smoothing algorithm
402 :
403 : // determinant
404 3290256 : const Real det = S.det();
405 3290256 : const Real det_sq = det * det;
406 3290256 : const Real det_cube = det_sq * det;
407 :
408 3290256 : const Real ref_vol_sq = _ref_vol * _ref_vol;
409 :
410 : // trace of S^T * S
411 : // DO NOT USE RealTensor.tr for the trace, it will NOT be correct for
412 : // 1D and 2D meshes because of our hack of putting 1s in the diagonal of
413 : // S for the extra dimensions (see get_jacobian_at_qp)
414 3290256 : const auto tr = trace(S.transpose() * S, dim);
415 3290256 : const Real tr_div_dim = tr / dim;
416 :
417 : // Precompute pow(tr_div_dim, 0.5 * dim - x) for x = 0, 1, 2
418 3290256 : const Real half_dim = 0.5 * dim;
419 : const std::vector<Real> trace_powers{
420 3290256 : std::pow(tr_div_dim, half_dim),
421 3290256 : std::pow(tr_div_dim, half_dim - 1.),
422 3290256 : std::pow(tr_div_dim, half_dim - 2.),
423 3564348 : };
424 :
425 : // inverse of S
426 3564348 : const RealTensor S_inv = S.inverse();
427 : // inverse transpose of S
428 548184 : const RealTensor S_inv_T = S_inv.transpose();
429 :
430 : // Identity matrix
431 5484144 : const RealTensor I(1, 0, 0,
432 5484144 : 0, 1, 0,
433 3290256 : 0, 0, 1);
434 :
435 : // The chi function allows us to handle degenerate elements
436 3290256 : const auto chi = chi_epsilon(det, _epsilon_squared_assembly);
437 3290256 : const Real chi_sq = chi * chi;
438 3290256 : const Real sqrt_term = std::sqrt(_epsilon_squared_assembly + det_sq);
439 : // dchi(x) / dx
440 3290256 : const Real chi_prime = 0.5 * (1. + det / sqrt_term);
441 3290256 : const Real chi_prime_sq = chi_prime * chi_prime;
442 : // d2chi(x) / dx2
443 3290256 : const Real chi_2prime = 0.5 * (1. / sqrt_term - det_sq / Utility::pow<3>(sqrt_term));
444 :
445 : // Distortion metric (beta)
446 : //const Real beta = trace_powers[0] / chi;
447 4386624 : const RealTensor dbeta_dS = (trace_powers[1] / chi) * S - (trace_powers[0] / chi_sq * chi_prime * det) * S_inv_T;
448 :
449 : // Dilation metric (mu)
450 : //const Real mu = 0.5 * (_ref_vol + det_sq / _ref_vol) / chi;
451 : // We represent d mu / dS as alpha(S) * S^-T, where alpha is a scalar function
452 3290256 : const Real alpha = (-chi_prime * det_cube + 2. * det_sq * chi - ref_vol_sq * det * chi_prime) / (2. * _ref_vol * chi_sq);
453 3290256 : const RealTensor dmu_dS = alpha * S_inv_T;
454 :
455 : // Combined metric (E)
456 : //const Real E = distortion_weight * beta + _dilation_weight * mu;
457 4112532 : const RealTensor dE_dS = distortion_weight * dbeta_dS + _dilation_weight * dmu_dS;
458 :
459 : // This vector is useful in computing dS/dR below
460 14257392 : std::vector<std::vector<std::vector<Real>>> dphi_maps = {dphidxi_map, dphideta_map, dphidzeta_map};
461 :
462 : // Compute residual (i.e., the gradient of the combined metric w.r.t node locations)
463 : // Recall that when the gradient (residual) is zero, the combined metric is minimized
464 37805760 : for (const auto l : elem.node_index_range())
465 : {
466 137285472 : for (const auto var_id : make_range(dim))
467 : {
468 : // Build dS/dR, the derivative of the physical-to-reference mapping Jacobin w.r.t. the mesh node locations
469 94206572 : RealTensor dS_dR = RealTensor(0);
470 409542624 : for (const auto jj : make_range(dim))
471 409024064 : dS_dR(var_id, jj) = dphi_maps[jj][l][qp];
472 :
473 : // Residual contribution. The contraction of dE/dS and dS/dR gives us
474 : // the gradient we are looking for, dE/dR
475 214103332 : F[var_id](l) += quad_weights[qp] * dE_dS.contract(dS_dR);
476 : }// for var_id
477 : }// for l
478 :
479 :
480 3290256 : if (request_jacobian)
481 : {
482 : // Compute jacobian of the smoothing system (i.e., the Hessian of the
483 : // combined metric w.r.t. the mesh node locations)
484 :
485 : // Precompute coefficients to be applied to each component of tensor
486 : // products in the loops below. At first glance, these coefficients look
487 : // like gibberish, but everything in the Hessian has been verified by
488 : // taking finite differences of the gradient. We should probably write
489 : // down the derivations of the gradient and Hessian somewhere...
490 :
491 : // Recall that above, dbeta_dS takes the form:
492 : // d(beta)/dS = c1(S) * S - c2(S) * S_inv_T,
493 : // where c1 and c2 are scalar-valued functions.
494 : const std::vector<Real> d2beta_dS2_coefs_times_distortion_weight = {
495 : //Part 1: scaler coefficients of d(c1 * S) / dS
496 : //
497 : // multiplies I[i,a] x I[j,b]
498 1630408 : (trace_powers[1] / chi) * distortion_weight,
499 : // multiplies S[a,b] x S[i,j]
500 1766270 : (((dim - 2.) / dim) * trace_powers[2] / chi) * distortion_weight,
501 : // multiplies S_inv[b,a] * S[i,j]
502 1766270 : (-(trace_powers[1] / chi_sq) * chi_prime * det) * distortion_weight,
503 : //
504 : //Part 2: scaler coefficients of d(-c2 * S_inv_T) / dS
505 : //
506 : // multiplies S[a,b] x S_inv[j,i]
507 1766270 : (-(trace_powers[1] / chi_sq) * chi_prime * det) * distortion_weight,
508 : // multiplies S_inv[b,a] x S_inv[j,i]
509 1766270 : (trace_powers[0] * (det / chi_sq)
510 1630408 : * ((2. * chi_prime_sq / chi - chi_2prime) * det - chi_prime)) * distortion_weight,
511 : // multiplies S_inv[b,i] x S_inv[j,a]
512 1766270 : ((trace_powers[0] / chi_sq) * chi_prime * det) * distortion_weight,
513 1766270 : };
514 :
515 : // d alpha / dS has the form c(S) * S^-T, where c is the scalar coefficient defined below
516 1902132 : const Real dalpha_dS_coef_times_dilation_weight = ((det / (2. * _ref_vol * chi_sq))
517 1902132 : * (-4. * _ref_vol * alpha * chi * chi_prime - chi_2prime * det_cube
518 1902132 : - chi_prime * det_sq + 4 * chi * det - ref_vol_sq * (chi_prime + det * chi_2prime))) * _dilation_weight;
519 :
520 : // This is also useful to precompute
521 1630408 : const Real alpha_times_dilation_weight = alpha * _dilation_weight;
522 :
523 : /*
524 :
525 : To increase the efficiency of the Jacobian computation, we take
526 : advantage of l-p symmetry, ij-ab symmetry, and the sparsity pattern of
527 : dS_dR. We also factor all possible multipliers out of inner loops for
528 : efficiency. The result is code that is more difficult to read. For
529 : clarity, consult the pseudo-code below in this comment.
530 :
531 : for (const auto l: elem.node_index_range()) // Contribution to Hessian
532 : from node l
533 : {
534 : for (const auto var_id1 : make_range(dim)) // Contribution from each
535 : x/y/z component of node l
536 : {
537 : // Build dS/dR_l, the derivative of the physical-to-reference
538 : mapping Jacobin w.r.t.
539 : // the l-th node
540 : RealTensor dS_dR_l = RealTensor(0);
541 : for (const auto ii : make_range(dim))
542 : dS_dR_l(var_id1, ii) = dphi_maps[ii][l][qp];
543 :
544 : for (const auto p: elem.node_index_range()) // Contribution to
545 : Hessian from node p
546 : {
547 : for (const auto var_id2 : make_range(dim)) // Contribution from
548 : each x/y/z component of node p
549 : {
550 : // Build dS/dR_l, the derivative of the physical-to-reference
551 : mapping Jacobin w.r.t.
552 : // the p-th node
553 : RealTensor dS_dR_p = RealTensor(0);
554 : for (const auto jj : make_range(dim))
555 : dS_dR_p(var_id2, jj) = dphi_maps[jj][p][qp];
556 :
557 : Real d2beta_dR2 = 0.;
558 : Real d2mu_dR2 = 0.;
559 : // Perform tensor contraction
560 : for (const auto i : make_range(dim))
561 : {
562 : for (const auto j : make_range(dim))
563 : {
564 : for (const auto a : make_range(dim))
565 : {
566 : for (const auto b : make_range(dim))
567 : {
568 : // Nasty tensor products to be multiplied by
569 : d2beta_dS2_coefs to get d2(beta) / dS2 const std::vector<Real>
570 : d2beta_dS2_tensor_contributions =
571 : {
572 : I(i,a) * I(j,b),
573 : S(a,b) * S(i,j),
574 : S_inv(b,a) * S(i,j),
575 : S(a,b) * S_inv(j,i),
576 : S_inv(b,a) * S_inv(j,i),
577 : S_inv(j,a) * S_inv(b,i),
578 : };
579 :
580 : // Combine precomputed coefficients with tensor products
581 : to get d2(beta) / dS2 Real d2beta_dS2 = 0.; for (const auto comp_id :
582 : index_range(d2beta_dS2_coefs))
583 : {
584 : const Real contribution = d2beta_dS2_coefs[comp_id] *
585 : d2beta_dS2_tensor_contributions[comp_id]; d2beta_dS2 += contribution;
586 : }
587 :
588 : // Incorporate tensor product portion to get d2(mu) /
589 : dS2 const Real d2mu_dS2 = dalpha_dS_coef * S_inv(b,a) * S_inv(j,i) -
590 : alpha * S_inv(b,i) * S_inv(j,a);
591 :
592 : // Chain rule to change d/dS to d/dR
593 : d2beta_dR2 += d2beta_dS2 * dS_dR_l(a, b) * dS_dR_p(i,
594 : j); d2mu_dR2 += d2mu_dS2 * dS_dR_l(a, b) * dS_dR_p(i, j);
595 :
596 : }// for b
597 : }// for a
598 : }// for j
599 : }// for i, end tensor contraction
600 :
601 : // Jacobian contribution
602 : K[var_id1][var_id2](l, p) += quad_weights[qp] * ((1. -
603 : _dilation_weight) * d2beta_dR2 + _dilation_weight * d2mu_dR2);
604 :
605 : }// for var_id2
606 : }// for p
607 : }// for var_id1
608 : }// for l
609 :
610 : End pseudo-code, begin efficient code
611 :
612 : */
613 :
614 18590816 : for (const auto l: elem.node_index_range()) // Contribution to Hessian from node l
615 : {
616 67470768 : for (const auto var_id1 : make_range(dim)) // Contribution from each x/y/z component of node l
617 : {
618 : // Build dS/dR_l, the derivative of the physical-to-reference mapping Jacobin w.r.t.
619 : // the l-th node
620 50510360 : RealTensor dS_dR_l = RealTensor(0);
621 201307632 : for (const auto ii : make_range(dim))
622 201062688 : dS_dR_l(var_id1, ii) = dphi_maps[ii][l][qp];
623 :
624 : // Jacobian is symmetric, only need to loop over lower triangular portion
625 429500680 : for (const auto p: make_range(l + 1)) // Contribution to Hessian from node p
626 : {
627 1514151456 : for (const auto var_id2 : make_range(dim)) // Contribution from each x/y/z component of node p
628 : {
629 : // Build dS/dR_l, the derivative of the physical-to-reference mapping Jacobin w.r.t.
630 : // the p-th node
631 1135161136 : RealTensor dS_dR_p = RealTensor(0);
632 4537039584 : for (const auto jj : make_range(dim))
633 4535836224 : dS_dR_p(var_id2, jj) = dphi_maps[jj][p][qp];
634 :
635 94596548 : Real d2E_dR2 = 0.;
636 : // Perform tensor contraction
637 4537039584 : for (const auto i : make_range(dim))
638 : {
639 :
640 13600318560 : for (const auto j : make_range(dim))
641 : {
642 :
643 10198440112 : const auto S_ij = S(i,j);
644 10198440112 : const auto S_inv_ji = S_inv(j,i);
645 :
646 : // Apply the stuff only depending on i and j before entering a, b loops
647 : // beta
648 : const std::vector<Real> d2beta_dS2_coefs_ij_applied{
649 10198440112 : d2beta_dS2_coefs_times_distortion_weight[1] * S_ij,
650 11048309268 : d2beta_dS2_coefs_times_distortion_weight[2] * S_ij,
651 11048309268 : d2beta_dS2_coefs_times_distortion_weight[3] * S_inv_ji,
652 11048309268 : d2beta_dS2_coefs_times_distortion_weight[4] * S_inv_ji,
653 10198440112 : };
654 : // mu
655 10198440112 : const auto dalpha_dS_coef_ij_applied = dalpha_dS_coef_times_dilation_weight * S_inv_ji;
656 :
657 849869156 : Real d2E_dSdR_l = 0.;
658 849869156 : Real d2E_dSdR_p = 0.;
659 :
660 30588132448 : for (const auto a : make_range(i + 1))
661 : {
662 :
663 : // If this condition is met, both the ijab and abij
664 : // contributions to the Jacobian are zero due to the
665 : // spasity patterns of dS_dR_l and dS_dR_p and this
666 : // iteration may be skipped
667 20389692336 : if (!(a == var_id1 && i == var_id2) &&
668 17083158544 : !(a == var_id2 && i == var_id1))
669 15572163584 : continue;
670 :
671 3401878448 : const auto S_inv_ja = S_inv(j,a);
672 :
673 3401878448 : const Real d2beta_dS2_coef_ia_applied = d2beta_dS2_coefs_times_distortion_weight[0] * I(i,a);
674 3401878448 : const Real d2beta_dS2_coef_ja_applied = d2beta_dS2_coefs_times_distortion_weight[5] * S_inv_ja;
675 3401878448 : const Real alpha_ja_applied = alpha_times_dilation_weight * S_inv_ja;
676 :
677 3401878448 : const auto b_limit = (a == i) ? j + 1 : dim;
678 12466959904 : for (const auto b : make_range(b_limit))
679 : {
680 :
681 : // Combine precomputed coefficients with tensor products
682 : // to get d2(beta) / dS2
683 : Real d2beta_dS2_times_distortion_weight = (
684 9820504164 : d2beta_dS2_coef_ia_applied * I(j,b) +
685 9065081456 : d2beta_dS2_coefs_ij_applied[0] * S(a,b) +
686 9065081456 : d2beta_dS2_coefs_ij_applied[1] * S_inv(b,a) +
687 9820504164 : d2beta_dS2_coefs_ij_applied[2] * S(a,b) +
688 9065081456 : d2beta_dS2_coefs_ij_applied[3] * S_inv(b,a) +
689 9065081456 : d2beta_dS2_coef_ja_applied * S_inv(b,i)
690 9065081456 : );
691 :
692 : // Incorporate tensor product portion to get d2(mu) /
693 : // dS2
694 9065081456 : const Real d2mu_dS2_times_dilation_weight = dalpha_dS_coef_ij_applied * S_inv(b,a) - alpha_ja_applied * S_inv(b,i);
695 :
696 :
697 : // Chain rule to change d/dS to d/dR
698 9065081456 : const auto d2E_dS2 =
699 : d2beta_dS2_times_distortion_weight +
700 : d2mu_dS2_times_dilation_weight;
701 :
702 : // if !(a == var_id1 (next line) && i == var_id2
703 : // (outside 'a' loop)), dS_dR_l(p) multiplier is zero
704 9065081456 : d2E_dSdR_l += d2E_dS2 * dS_dR_l(a, b);
705 :
706 9065081456 : if (!(i == a && j == b))
707 : // if !(a == var_id2 (next line) && i == var_id1
708 : // (outside 'a' loop)), dS_dR_p(l) multiplier is zero
709 7929920320 : d2E_dSdR_p += d2E_dS2 * dS_dR_p(a, b);
710 :
711 : } // for b
712 : } // for a
713 10198440112 : d2E_dR2 +=
714 10198440112 : d2E_dSdR_l * dS_dR_p(i, j) + d2E_dSdR_p * dS_dR_l(i, j);
715 : }// for j
716 : }// for i, end tensor contraction
717 :
718 : // Jacobian contribution
719 1135161136 : const Real jacobian_contribution = quad_weights[qp] * d2E_dR2;
720 1135161136 : K[var_id1][var_id2](l, p) += jacobian_contribution;
721 : // Jacobian is symmetric, add contribution to p,l entry
722 : // Don't get the diagonal twice!
723 1135161136 : if (p < l)
724 : // Note the transposition of var_id1 and var_id2 as these are also jacobian indices
725 1066394058 : K[var_id2][var_id1](p, l) += jacobian_contribution;
726 :
727 : }// for var_id2
728 : }// for p
729 : }// for var_id1
730 : }// for l
731 : }
732 2742072 : } // end of the quadrature point qp-loop
733 :
734 302616 : return request_jacobian;
735 2742072 : }
736 :
737 2840 : const MeshQualityInfo & VariationalSmootherSystem::get_mesh_info()
738 : {
739 2840 : if (!_mesh_info.initialized)
740 2840 : compute_mesh_quality_info();
741 :
742 2840 : return _mesh_info;
743 : }
744 :
745 38120 : void VariationalSmootherSystem::compute_mesh_quality_info()
746 : {
747 : // If the reference volume has not yet been computed, compute it.
748 39188 : if (std::abs(_ref_vol) < TOLERANCE * TOLERANCE)
749 0 : prepare_for_smoothing();
750 :
751 39188 : std::unique_ptr<DiffContext> con = this->build_context();
752 1068 : FEMContext & femcontext = cast_ref<FEMContext &>(*con);
753 38120 : this->init_context(femcontext);
754 :
755 2136 : const auto & mesh = this->get_mesh();
756 38120 : const auto dim = mesh.mesh_dimension();
757 38120 : const Real half_dim = 0.5 * dim;
758 38120 : const auto distortion_weight = 1. - _dilation_weight;
759 :
760 : // Make pre-requests before reinit() for efficiency in
761 : // --enable-deprecated builds, and to avoid errors in
762 : // --disable-deprecated builds.
763 1068 : const auto & fe_map = femcontext.get_element_fe(0)->get_fe_map();
764 1068 : const auto & JxW = fe_map.get_JxW();
765 1068 : fe_map.get_dxyzdxi();
766 1068 : fe_map.get_dxyzdeta();
767 1068 : fe_map.get_dxyzdzeta();
768 :
769 38120 : MeshQualityInfo info;
770 :
771 619412 : for (const auto * elem : mesh.active_local_element_ptr_range())
772 : {
773 296832 : femcontext.pre_fe_reinit(*this, elem);
774 296832 : femcontext.elem_fe_reinit();
775 :
776 : // Element-integrated quantities
777 24712 : Real det_S_int = 0.;
778 24712 : Real beta_int = 0.;
779 24712 : Real mu_int = 0.;
780 24712 : Real combined_int = 0.;
781 :
782 3790416 : for (const auto qp : index_range(JxW))
783 : {
784 3784620 : const auto det_SxW = JxW[qp] * _target_jacobian_dets[elem->type()][qp];
785 3493584 : det_S_int += det_SxW;
786 :
787 : // Grab the physical-to-reference mapping Jacobian matrix (i.e., "S") at this qp
788 3493584 : RealTensor S = get_jacobian_at_qp(fe_map, dim, qp);
789 :
790 : // Apply target element transformation
791 3493584 : S *= _target_jacobians[elem->type()][qp];
792 :
793 : // Determinant of S
794 3493584 : const auto det = S.det();
795 3493584 : const auto det_sq = det * det;
796 :
797 3493584 : if (det > info.max_qp_det_S)
798 128353 : info.max_qp_det_S = det;
799 3365231 : else if (det < info.min_qp_det_S)
800 156849 : info.min_qp_det_S = det;
801 :
802 3493584 : if (det < TOLERANCE * TOLERANCE)
803 1356 : info.mesh_is_tangled = true;
804 :
805 : // trace of S^T * S
806 3493584 : const auto tr = trace(S.transpose() * S, dim);
807 :
808 : // The chi function allows us to handle degenerate elements
809 3493584 : const auto chi = chi_epsilon(det, _epsilon_squared_assembly);
810 :
811 : // distortion
812 3493584 : const Real beta = std::pow(tr / dim, half_dim) / chi;
813 3493584 : beta_int += beta * det_SxW;
814 :
815 : // dilation
816 3493584 : const Real mu = 0.5 * (_ref_vol + det_sq / _ref_vol) / chi;
817 3493584 : mu_int += mu * det_SxW;
818 :
819 : // combined
820 3493584 : const Real E = distortion_weight * beta + _dilation_weight * mu;
821 3493584 : combined_int += E * det_SxW;
822 : }
823 :
824 296832 : info.total_det_S += det_S_int;
825 296832 : if (det_S_int > info.max_elem_det_S.first)
826 5492 : info.max_elem_det_S = std::make_pair(det_S_int, elem->id());
827 235331 : else if (det_S_int < info.min_elem_det_S.first)
828 6042 : info.min_elem_det_S = std::make_pair(det_S_int, elem->id());
829 :
830 296832 : info.total_distortion += beta_int;
831 296832 : if (beta_int > info.max_elem_distortion.first)
832 5383 : info.max_elem_distortion = std::make_pair(beta_int, elem->id());
833 236161 : else if (beta_int < info.min_elem_distortion.first)
834 6285 : info.min_elem_distortion = std::make_pair(beta_int, elem->id());
835 :
836 296832 : info.total_dilation += mu_int;
837 296832 : if (mu_int > info.max_elem_dilation.first)
838 5475 : info.max_elem_dilation = std::make_pair(mu_int, elem->id());
839 235664 : else if (mu_int < info.min_elem_dilation.first)
840 6192 : info.min_elem_dilation = std::make_pair(mu_int, elem->id());
841 :
842 296832 : info.total_combined += combined_int;
843 296832 : if (combined_int > info.max_elem_combined.first)
844 5383 : info.max_elem_combined = std::make_pair(combined_int, elem->id());
845 235968 : else if (combined_int < info.min_elem_combined.first)
846 6249 : info.min_elem_combined = std::make_pair(combined_int, elem->id());
847 :
848 35984 : } // for elem
849 :
850 : // Get contributions from elements on other processors
851 38120 : communicate_pair_max(info.max_elem_det_S, mesh.comm());
852 38120 : communicate_pair_min(info.min_elem_det_S, mesh.comm());
853 38120 : mesh.comm().max(info.max_qp_det_S);
854 38120 : mesh.comm().min(info.min_qp_det_S);
855 38120 : mesh.comm().sum(info.total_det_S);
856 :
857 38120 : communicate_pair_max(info.max_elem_distortion, mesh.comm());
858 38120 : communicate_pair_min(info.min_elem_distortion, mesh.comm());
859 38120 : mesh.comm().sum(info.total_distortion);
860 :
861 38120 : communicate_pair_max(info.max_elem_dilation, mesh.comm());
862 38120 : communicate_pair_min(info.min_elem_dilation, mesh.comm());
863 38120 : mesh.comm().sum(info.total_dilation);
864 :
865 38120 : communicate_pair_max(info.max_elem_combined, mesh.comm());
866 38120 : communicate_pair_min(info.min_elem_combined, mesh.comm());
867 38120 : mesh.comm().sum(info.total_combined);
868 :
869 38120 : mesh.comm().max(info.mesh_is_tangled);
870 :
871 38120 : _mesh_info = info;
872 38120 : }
873 :
874 : std::pair<std::unique_ptr<Elem>, std::vector<std::unique_ptr<Node>>>
875 1036 : VariationalSmootherSystem::get_target_elem(const ElemType & type)
876 : {
877 : // Build target element
878 1074 : auto target_elem = Elem::build(type);
879 :
880 : // Volume of reference element
881 1036 : const auto ref_vol = target_elem->reference_elem()->volume();
882 :
883 : // Update the nodes of the target element, depending on type
884 38 : const Real sqrt_3 = std::sqrt(Real(3));
885 114 : std::vector<std::unique_ptr<Node>> owned_nodes;
886 :
887 1074 : const auto type_str = Utility::enum_to_string(type);
888 :
889 : // Elems deriving from Tri
890 1036 : if (type_str.compare(0, 3, "TRI") == 0)
891 : {
892 :
893 : // The target element will be an equilateral triangle with area equal to
894 : // the area of the reference element.
895 :
896 : // Equilateral triangle side length preserving area of the reference element
897 193 : const auto side_length = std::sqrt(4. / sqrt_3 * ref_vol);
898 :
899 : // Define the nodal locations of the vertices
900 6 : const auto & s = side_length;
901 : // x y node_id
902 199 : owned_nodes.emplace_back(Node::build(Point(0., 0.), 0));
903 193 : owned_nodes.emplace_back(Node::build(Point(s, 0.), 1));
904 199 : owned_nodes.emplace_back(Node::build(Point(0.5 * s, 0.5 * sqrt_3 * s), 2));
905 :
906 193 : switch (type)
907 : {
908 4 : case TRI3: {
909 : // Nothing to do here, vertices already added above
910 4 : break;
911 : }
912 :
913 55 : case TRI6: {
914 : // Define the midpoint nodes of the equilateral triangle
915 : // x y node_id
916 55 : owned_nodes.emplace_back(Node::build(Point(0.50 * s, 0.00), 3));
917 57 : owned_nodes.emplace_back(Node::build(Point(0.75 * s, 0.25 * sqrt_3 * s), 4));
918 57 : owned_nodes.emplace_back(Node::build(Point(0.25 * s, 0.25 * sqrt_3 * s), 5));
919 :
920 55 : break;
921 : }
922 :
923 0 : default:
924 0 : libmesh_error_msg("Unsupported triangular element: " << type_str);
925 : break;
926 : }
927 : } // if Tri
928 :
929 :
930 : // Elems deriving from Pyramid
931 843 : else if (type_str.compare(0, 7, "PYRAMID") == 0)
932 : {
933 :
934 : // The target element is a pyramid with an square base and
935 : // equilateral triangular sides with volume equal to the volume of the
936 : // reference element.
937 :
938 : // A pyramid with square base sidelength s and equilateral triangular
939 : // sides has height h = s / sqrt(2).
940 : // The volume is v = s^2 h / 3 = s^3 / ( 3 sqrt(2)).
941 : // Solving for s: s = (3 sqrt(2) v)^(1/3), where v is the volume of the
942 : // non-optimal reference element.
943 :
944 10 : const Real sqrt_2 = std::sqrt(Real(2));
945 : // Side length that preserves the volume of the reference element
946 305 : const auto side_length = std::pow(3. * sqrt_2 * ref_vol, 1. / 3.);
947 : // Pyramid height with the property that all faces are equilateral triangles
948 305 : const auto target_height = side_length / sqrt_2;
949 :
950 10 : const auto & s = side_length;
951 10 : const auto & h = target_height;
952 :
953 : // x y z node_id
954 315 : owned_nodes.emplace_back(Node::build(Point(0., 0., 0.), 0));
955 315 : owned_nodes.emplace_back(Node::build(Point(s, 0., 0.), 1));
956 315 : owned_nodes.emplace_back(Node::build(Point(s, s, 0.), 2));
957 305 : owned_nodes.emplace_back(Node::build(Point(0., s, 0.), 3));
958 315 : owned_nodes.emplace_back(Node::build(Point(0.5 * s, 0.5 * s, h), 4));
959 :
960 305 : if (type == PYRAMID13 || type == PYRAMID14 || type == PYRAMID18)
961 : {
962 8 : const auto & on = owned_nodes;
963 : // Define the edge midpoint nodes of the pyramid
964 :
965 : // Base node to base node midpoint nodes
966 242 : owned_nodes.emplace_back(Node::build((*on[0] + *on[1]) / 2., 5));
967 242 : owned_nodes.emplace_back(Node::build((*on[1] + *on[2]) / 2., 6));
968 242 : owned_nodes.emplace_back(Node::build((*on[2] + *on[3]) / 2., 7));
969 242 : owned_nodes.emplace_back(Node::build((*on[3] + *on[0]) / 2., 8));
970 :
971 : // Base node to apex node midpoint nodes
972 242 : owned_nodes.emplace_back(Node::build(Point((*on[0] + *on[4]) / 2.), 9));
973 242 : owned_nodes.emplace_back(Node::build(Point((*on[1] + *on[4]) / 2.), 10));
974 242 : owned_nodes.emplace_back(Node::build(Point((*on[2] + *on[4]) / 2.), 11));
975 242 : owned_nodes.emplace_back(Node::build(Point((*on[3] + *on[4]) / 2.), 12));
976 :
977 234 : if (type == PYRAMID14 || type == PYRAMID18)
978 : {
979 : // Define the square face midpoint node of the pyramid
980 151 : owned_nodes.emplace_back(
981 169 : Node::build(Point((*on[0] + *on[1] + *on[2] + *on[3]) / 4.), 13));
982 :
983 163 : if (type == PYRAMID18)
984 : {
985 : // Define the triangular face nodes
986 96 : owned_nodes.emplace_back(Node::build(Point((*on[0] + *on[1] + *on[4]) / 3.), 14));
987 96 : owned_nodes.emplace_back(Node::build(Point((*on[1] + *on[2] + *on[4]) / 3.), 15));
988 96 : owned_nodes.emplace_back(Node::build(Point((*on[2] + *on[3] + *on[4]) / 3.), 16));
989 100 : owned_nodes.emplace_back(Node::build(Point((*on[3] + *on[0] + *on[4]) / 3.), 17));
990 : }
991 8 : }
992 : }
993 :
994 71 : else if (type != PYRAMID5)
995 0 : libmesh_error_msg("Unsupported pyramid element: " << type_str);
996 :
997 : } // if Pyramid
998 :
999 : // Set the target_elem equal to the reference elem
1000 : else
1001 7557 : for (const auto & node : target_elem->reference_elem()->node_ref_range())
1002 7513 : owned_nodes.emplace_back(Node::build(node, node.id()));
1003 :
1004 : // Set nodes of target element
1005 12705 : for (const auto & node_ptr : owned_nodes)
1006 12087 : target_elem->set_node(node_ptr->id(), node_ptr.get());
1007 :
1008 38 : libmesh_assert(relative_fuzzy_equals(target_elem->volume(), ref_vol, TOLERANCE));
1009 :
1010 1074 : return std::make_pair(std::move(target_elem), std::move(owned_nodes));
1011 960 : }
1012 :
1013 1036 : void VariationalSmootherSystem::get_target_to_reference_jacobian(
1014 : const Elem * const target_elem,
1015 : const FEMContext & femcontext,
1016 : std::vector<RealTensor> & jacobians,
1017 : std::vector<Real> & jacobian_dets)
1018 : {
1019 :
1020 1036 : const auto dim = target_elem->dim();
1021 :
1022 38 : const auto & qrule_points = femcontext.get_element_qrule().get_points();
1023 38 : const auto & qrule_weights = femcontext.get_element_qrule().get_weights();
1024 38 : const auto nq_points = femcontext.get_element_qrule().n_points();
1025 :
1026 : // If the target element is the reference element, Jacobian matrix is
1027 : // identity, det of inverse is 1. These will only be overwritten if a
1028 : // different target element is explicitly specified.
1029 1074 : jacobians = std::vector<RealTensor>(nq_points, RealTensor(
1030 : 1., 0., 0.,
1031 : 0., 1., 0.,
1032 38 : 0., 0., 1.));
1033 1036 : jacobian_dets = std::vector<Real>(nq_points, 1.0);
1034 :
1035 : // Don't use "if (*target_elem == *(target_elem->reference_elem()))" here, it
1036 : // only compares global node ids, not the node locations themselves.
1037 38 : bool target_equals_reference = true;
1038 1036 : const auto * ref_elem = target_elem->reference_elem();
1039 12705 : for (const auto local_id : make_range(target_elem->n_nodes()))
1040 11669 : target_equals_reference &= target_elem->node_ref(local_id) == ref_elem->node_ref(local_id);
1041 1036 : if (target_equals_reference)
1042 538 : return;
1043 :
1044 : // Create FEMap to compute target_element mapping information
1045 530 : FEMap fe_map_target;
1046 :
1047 : // pre-request mapping derivatives
1048 16 : fe_map_target.get_dxyzdxi();
1049 16 : fe_map_target.get_dxyzdeta();
1050 16 : fe_map_target.get_dxyzdzeta();
1051 :
1052 : // build map
1053 498 : fe_map_target.init_reference_to_physical_map(dim, qrule_points, target_elem);
1054 498 : fe_map_target.compute_map(dim, qrule_weights, target_elem, /*d2phi=*/false);
1055 :
1056 11725 : for (const auto qp : make_range(nq_points))
1057 : {
1058 : // We use Larisa's H notation to denote the reference-to-target jacobian
1059 11227 : RealTensor H = get_jacobian_at_qp(fe_map_target, dim, qp);
1060 :
1061 : // The target-to-reference jacobian is the inverse of the
1062 : // reference-to-target jacobian
1063 11227 : jacobians[qp] = H.inverse();
1064 11637 : jacobian_dets[qp] = jacobians[qp].det();
1065 : }
1066 466 : }
1067 :
1068 : } // namespace libMesh
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