refineable_solid_elements.cc
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26 // Non-inline member functions and static member data for refineable solid
27 // mechanics elements
28 
30 
31 namespace oomph
32 {
33  //====================================================================
34  /// Residuals for Refineable QPVDElements
35  //====================================================================
36  template<unsigned DIM>
39  DenseMatrix<double>& jacobian,
40  const unsigned& flag)
41  {
42 #ifdef PARANOID
43  // Check if the constitutive equation requires the explicit imposition of an
44  // incompressibility constraint
46  {
47  throw OomphLibError("RefineablePVDEquations cannot be used with "
48  "incompressible constitutive laws.",
49  OOMPH_CURRENT_FUNCTION,
50  OOMPH_EXCEPTION_LOCATION);
51  }
52 #endif
53 
54  // Simply set up initial condition?
55  if (Solid_ic_pt != 0)
56  {
57  get_residuals_for_solid_ic(residuals);
58  return;
59  }
60 
61  // Find out how many nodes there are
62  const unsigned n_node = nnode();
63 
64  // Find out how many positional dofs there are
65  const unsigned n_position_type = this->nnodal_position_type();
66 
67  // Integers to store local equation numbers
68  int local_eqn = 0;
69 
70  // Timescale ratio (non-dim density)
71  double lambda_sq = this->lambda_sq();
72 
73  // Time factor
74  double time_factor = 0.0;
75  if (lambda_sq > 0)
76  {
77  time_factor = this->node_pt(0)->position_time_stepper_pt()->weight(2, 0);
78  }
79 
80  // Set up memory for the shape functions
81  Shape psi(n_node, n_position_type);
82  DShape dpsidxi(n_node, n_position_type, DIM);
83 
84  // Set the value of n_intpt -- the number of integration points
85  const unsigned n_intpt = integral_pt()->nweight();
86 
87  // Set the vector to hold the local coordinates in the element
88  Vector<double> s(DIM);
89 
90  // Loop over the integration points
91  for (unsigned ipt = 0; ipt < n_intpt; ipt++)
92  {
93  // Assign the values of s
94  for (unsigned i = 0; i < DIM; ++i)
95  {
96  s[i] = integral_pt()->knot(ipt, i);
97  }
98 
99  // Get the integral weight
100  double w = integral_pt()->weight(ipt);
101 
102  // Call the derivatives of the shape functions (and get Jacobian)
103  double J = dshape_lagrangian_at_knot(ipt, psi, dpsidxi);
104 
105  // Calculate interpolated values of the derivative of global position
106  // wrt lagrangian coordinates
107  DenseMatrix<double> interpolated_G(DIM, DIM, 0.0);
108 
109  // Setup memory for accelerations
110  Vector<double> accel(DIM, 0.0);
111 
112  // Storage for Lagrangian coordinates (initialised to zero)
113  Vector<double> interpolated_xi(DIM, 0.0);
114 
115  // Calculate displacements and derivatives and lagrangian coordinates
116  for (unsigned l = 0; l < n_node; l++)
117  {
118  // Loop over positional dofs
119  for (unsigned k = 0; k < n_position_type; k++)
120  {
121  double psi_ = psi(l, k);
122  // Loop over displacement components (deformed position)
123  for (unsigned i = 0; i < DIM; i++)
124  {
125  // Calculate the Lagrangian coordinates and the accelerations
126  interpolated_xi[i] += lagrangian_position_gen(l, k, i) * psi_;
127 
128  // Only compute accelerations if inertia is switched on
129  // otherwise the timestepper might not be able to
130  // work out dx_gen_dt(2,...)
131  if ((lambda_sq > 0.0) && (this->Unsteady))
132  {
133  accel[i] += dnodal_position_gen_dt(2, l, k, i) * psi_;
134  }
135 
136  // Loop over derivative directions
137  for (unsigned j = 0; j < DIM; j++)
138  {
139  interpolated_G(j, i) +=
140  this->nodal_position_gen(l, k, i) * dpsidxi(l, k, j);
141  }
142  }
143  }
144  }
145 
146  // Get isotropic growth factor
147  double gamma = 1.0;
148  this->get_isotropic_growth(ipt, s, interpolated_xi, gamma);
149 
150  // Get body force at current time
151  Vector<double> b(DIM);
152  this->body_force(interpolated_xi, b);
153 
154  // We use Cartesian coordinates as the reference coordinate
155  // system. In this case the undeformed metric tensor is always
156  // the identity matrix -- stretched by the isotropic growth
157  double diag_entry = pow(gamma, 2.0 / double(DIM));
158  DenseMatrix<double> g(DIM);
159  for (unsigned i = 0; i < DIM; i++)
160  {
161  for (unsigned j = 0; j < DIM; j++)
162  {
163  if (i == j)
164  {
165  g(i, j) = diag_entry;
166  }
167  else
168  {
169  g(i, j) = 0.0;
170  }
171  }
172  }
173 
174  // Premultiply the undeformed volume ratio (from the isotropic
175  // growth), the weights and the Jacobian
176  double W = gamma * w * J;
177 
178  // Declare and calculate the deformed metric tensor
179  DenseMatrix<double> G(DIM);
180 
181  // Assign values of G
182  for (unsigned i = 0; i < DIM; i++)
183  {
184  // Do upper half of matrix
185  for (unsigned j = i; j < DIM; j++)
186  {
187  // Initialise G(i,j) to zero
188  G(i, j) = 0.0;
189  // Now calculate the dot product
190  for (unsigned k = 0; k < DIM; k++)
191  {
192  G(i, j) += interpolated_G(i, k) * interpolated_G(j, k);
193  }
194  }
195  // Matrix is symmetric so just copy lower half
196  for (unsigned j = 0; j < i; j++)
197  {
198  G(i, j) = G(j, i);
199  }
200  }
201 
202  // Now calculate the stress tensor from the constitutive law
203  DenseMatrix<double> sigma(DIM);
204  this->get_stress(g, G, sigma);
205 
206  // Get stress derivative by FD only needed for Jacobian
207  //-----------------------------------------------------
208 
209  // Stress derivative
210  RankFourTensor<double> d_stress_dG(DIM, DIM, DIM, DIM, 0.0);
211  // Derivative of metric tensor w.r.t. to nodal coords
212  RankFiveTensor<double> d_G_dX(
213  n_node, n_position_type, DIM, DIM, DIM, 0.0);
214 
215  // Get Jacobian too?
216  if (flag == 1)
217  {
218  // Derivative of metric tensor w.r.t. to discrete positional dofs
219  // NOTE: Since G is symmetric we only compute the upper triangle
220  // and DO NOT copy the entries across. Subsequent computations
221  // must (and, in fact, do) therefore only operate with upper
222  // triangular entries
223  for (unsigned ll = 0; ll < n_node; ll++)
224  {
225  for (unsigned kk = 0; kk < n_position_type; kk++)
226  {
227  for (unsigned ii = 0; ii < DIM; ii++)
228  {
229  for (unsigned aa = 0; aa < DIM; aa++)
230  {
231  for (unsigned bb = aa; bb < DIM; bb++)
232  {
233  d_G_dX(ll, kk, ii, aa, bb) =
234  interpolated_G(aa, ii) * dpsidxi(ll, kk, bb) +
235  interpolated_G(bb, ii) * dpsidxi(ll, kk, aa);
236  }
237  }
238  }
239  }
240  }
241 
242  // Get the "upper triangular"
243  // entries of the derivatives of the stress tensor with
244  // respect to G
245  this->get_d_stress_dG_upper(g, G, sigma, d_stress_dG);
246  }
247 
248 
249  // Add pre-stress
250  for (unsigned i = 0; i < DIM; i++)
251  {
252  for (unsigned j = 0; j < DIM; j++)
253  {
254  sigma(i, j) += this->prestress(i, j, interpolated_xi);
255  }
256  }
257 
258  //=====EQUATIONS OF ELASTICITY FROM PRINCIPLE OF VIRTUAL
259  // DISPLACEMENTS========
260 
261 
262  // Default setting for non-hanging node
263  unsigned n_master = 1;
264  double hang_weight = 1.0;
265 
266  // Loop over the test functions, nodes of the element
267  for (unsigned l = 0; l < n_node; l++)
268  {
269  // Get pointer to local node l
270  Node* local_node_pt = node_pt(l);
271 
272  // Cache hang status
273  bool is_hanging = local_node_pt->is_hanging();
274 
275  // If the node is a hanging node
276  if (is_hanging)
277  {
278  n_master = local_node_pt->hanging_pt()->nmaster();
279  }
280  // Otherwise the node is its own master
281  else
282  {
283  n_master = 1;
284  }
285 
286 
287  // Storage for local equation numbers at node indexed by
288  // type and direction
289  DenseMatrix<int> position_local_eqn_at_node(n_position_type, DIM);
290 
291  // Loop over the master nodes
292  for (unsigned m = 0; m < n_master; m++)
293  {
294  if (is_hanging)
295  {
296  // Find the equation numbers
297  position_local_eqn_at_node = local_position_hang_eqn(
298  local_node_pt->hanging_pt()->master_node_pt(m));
299 
300  // Find the hanging node weight
301  hang_weight = local_node_pt->hanging_pt()->master_weight(m);
302  }
303  else
304  {
305  // Loop of types of dofs
306  for (unsigned k = 0; k < n_position_type; k++)
307  {
308  // Loop over the displacement components
309  for (unsigned i = 0; i < DIM; i++)
310  {
311  position_local_eqn_at_node(k, i) = position_local_eqn(l, k, i);
312  }
313  }
314 
315  // Hang weight is one
316  hang_weight = 1.0;
317  }
318 
319  // Loop of types of dofs
320  for (unsigned k = 0; k < n_position_type; k++)
321  {
322  // Offset for faster access
323  const unsigned offset5 = dpsidxi.offset(l, k);
324 
325  // Loop over the displacement components
326  for (unsigned i = 0; i < DIM; i++)
327  {
328  local_eqn = position_local_eqn_at_node(k, i);
329 
330  /*IF it's not a boundary condition*/
331  if (local_eqn >= 0)
332  {
333  // Initialise the contribution
334  double sum = 0.0;
335 
336  // Acceleration and body force
337  sum += (lambda_sq * accel[i] - b[i]) * psi(l, k);
338 
339  // Stress term
340  for (unsigned a = 0; a < DIM; a++)
341  {
342  unsigned count = offset5;
343  for (unsigned b = 0; b < DIM; b++)
344  {
345  // Add the stress terms to the residuals
346  sum += sigma(a, b) * interpolated_G(a, i) *
347  dpsidxi.raw_direct_access(count);
348  ++count;
349  }
350  }
351  residuals[local_eqn] += W * sum * hang_weight;
352 
353 
354  // Get Jacobian too?
355  if (flag == 1)
356  {
357  // Offset for faster access in general stress loop
358  const unsigned offset1 = d_G_dX.offset(l, k, i);
359 
360  // Default setting for non-hanging node
361  unsigned nn_master = 1;
362  double hhang_weight = 1.0;
363 
364  // Loop over the nodes of the element again
365  for (unsigned ll = 0; ll < n_node; ll++)
366  {
367  // Get pointer to local node ll
368  Node* llocal_node_pt = node_pt(ll);
369 
370  // Cache hang status
371  bool iis_hanging = llocal_node_pt->is_hanging();
372 
373  // If the node is a hanging node
374  if (iis_hanging)
375  {
376  nn_master = llocal_node_pt->hanging_pt()->nmaster();
377  }
378  // Otherwise the node is its own master
379  else
380  {
381  nn_master = 1;
382  }
383 
384 
385  // Storage for local unknown numbers at node indexed by
386  // type and direction
387  DenseMatrix<int> position_local_unk_at_node(n_position_type,
388  DIM);
389 
390  // Loop over the master nodes
391  for (unsigned mm = 0; mm < nn_master; mm++)
392  {
393  if (iis_hanging)
394  {
395  // Find the unknown numbers
396  position_local_unk_at_node = local_position_hang_eqn(
397  llocal_node_pt->hanging_pt()->master_node_pt(mm));
398 
399  // Find the hanging node weight
400  hhang_weight =
401  llocal_node_pt->hanging_pt()->master_weight(mm);
402  }
403  else
404  {
405  // Loop of types of dofs
406  for (unsigned kk = 0; kk < n_position_type; kk++)
407  {
408  // Loop over the displacement components
409  for (unsigned ii = 0; ii < DIM; ii++)
410  {
411  position_local_unk_at_node(kk, ii) =
412  position_local_eqn(ll, kk, ii);
413  }
414  }
415 
416  // Hang weight is one
417  hhang_weight = 1.0;
418  }
419 
420 
421  // Loop of types of dofs again
422  for (unsigned kk = 0; kk < n_position_type; kk++)
423  {
424  // Loop over the displacement components again
425  for (unsigned ii = 0; ii < DIM; ii++)
426  {
427  // Get the number of the unknown
428  int local_unknown =
429  position_local_unk_at_node(kk, ii);
430 
431 
432  /*IF it's not a boundary condition*/
433  if (local_unknown >= 0)
434  {
435  // Offset for faster access in general stress loop
436  const unsigned offset2 = d_G_dX.offset(ll, kk, ii);
437  const unsigned offset4 = dpsidxi.offset(ll, kk);
438 
439 
440  // General stress term
441  //--------------------
442  double sum = 0.0;
443  unsigned count1 = offset1;
444  for (unsigned a = 0; a < DIM; a++)
445  {
446  // Bump up direct access because we're only
447  // accessing upper triangle
448  count1 += a;
449  for (unsigned b = a; b < DIM; b++)
450  {
451  double factor =
452  d_G_dX.raw_direct_access(count1);
453  if (a == b) factor *= 0.5;
454 
455  // Offset for faster access
456  unsigned offset3 = d_stress_dG.offset(a, b);
457  unsigned count2 = offset2;
458  unsigned count3 = offset3;
459 
460  for (unsigned aa = 0; aa < DIM; aa++)
461  {
462  // Bump up direct access because we're only
463  // accessing upper triangle
464  count2 += aa;
465  count3 += aa;
466 
467  // Only upper half of derivatives w.r.t.
468  // symm tensor
469  for (unsigned bb = aa; bb < DIM; bb++)
470  {
471  sum +=
472  factor *
473  d_stress_dG.raw_direct_access(count3) *
474  d_G_dX.raw_direct_access(count2);
475  ++count2;
476  ++count3;
477  }
478  }
479  ++count1;
480  }
481  }
482 
483  // Multiply by weight and add contribution
484  // (Add directly because this bit is nonsymmetric)
485  jacobian(local_eqn, local_unknown) +=
486  sum * W * hang_weight * hhang_weight;
487 
488  // Only upper triangle (no separate test for bc as
489  // local_eqn is already nonnegative)
490  if ((i == ii) && (local_unknown >= local_eqn))
491  {
492  // Initialise the contribution
493  double sum = 0.0;
494 
495  // Inertia term
496  sum += lambda_sq * time_factor * psi(ll, kk) *
497  psi(l, k);
498 
499  // Stress term
500  unsigned count4 = offset4;
501  for (unsigned a = 0; a < DIM; a++)
502  {
503  // Cache term
504  const double factor =
505  dpsidxi.raw_direct_access(count4); // ll ,kk
506  ++count4;
507 
508  unsigned count5 = offset5;
509  for (unsigned b = 0; b < DIM; b++)
510  {
511  sum +=
512  sigma(a, b) * factor *
513  dpsidxi.raw_direct_access(count5); // l ,k
514  ++count5;
515  }
516  }
517 
518  // Multiply by weights to form contribution
519  double sym_entry =
520  sum * W * hang_weight * hhang_weight;
521  // Add contribution to jacobian
522  jacobian(local_eqn, local_unknown) += sym_entry;
523  // Add to lower triangular entries
524  if (local_eqn != local_unknown)
525  {
526  jacobian(local_unknown, local_eqn) += sym_entry;
527  }
528  }
529  } // End of if not boundary condition
530  }
531  }
532  }
533  }
534  }
535 
536  } // End of if not boundary condition
537 
538  } // End of loop over coordinate directions
539  } // End of loop over type of dof
540  } // End of loop over master nodes
541  } // End of loop over nodes
542  } // End of loop over integration points
543  }
544 
545 
546  //=======================================================================
547  /// Compute the diagonal of the velocity mass matrix for LSC
548  /// preconditioner.
549  //=======================================================================
550  template<unsigned DIM>
552  Vector<double>& mass_diag)
553  {
554  // Resize and initialise
555  mass_diag.assign(this->ndof(), 0.0);
556 
557  // find out how many nodes there are
558  unsigned n_node = this->nnode();
559 
560  // Find out how many position types of dof there are
561  const unsigned n_position_type = this->nnodal_position_type();
562 
563  // Set up memory for the shape functions
564  Shape psi(n_node, n_position_type);
565  DShape dpsidxi(n_node, n_position_type, DIM);
566 
567  // Number of integration points
568  unsigned n_intpt = this->integral_pt()->nweight();
569 
570  // Integer to store the local equations no
571  int local_eqn = 0;
572 
573  // Loop over the integration points
574  for (unsigned ipt = 0; ipt < n_intpt; ipt++)
575  {
576  // Get the integral weight
577  double w = this->integral_pt()->weight(ipt);
578 
579  // Call the derivatives of the shape functions
580  double J = this->dshape_lagrangian_at_knot(ipt, psi, dpsidxi);
581 
582  // Premultiply weights and Jacobian
583  double W = w * J;
584 
585  unsigned n_master = 1;
586  double hang_weight = 1.0;
587 
588  // Loop over the nodes
589  for (unsigned l = 0; l < n_node; l++)
590  {
591  // Get pointer to local node l
592  Node* local_node_pt = node_pt(l);
593 
594  // Cache hang status
595  bool is_hanging = local_node_pt->is_hanging();
596 
597  // If the node is a hanging node
598  if (is_hanging)
599  {
600  n_master = local_node_pt->hanging_pt()->nmaster();
601  }
602  // Otherwise the node is its own master
603  else
604  {
605  n_master = 1;
606  }
607 
608  // Storage for local equation numbers at node indexed by
609  // type and direction
610  DenseMatrix<int> position_local_eqn_at_node(n_position_type, DIM);
611 
612  // Loop over the master nodes
613  for (unsigned m = 0; m < n_master; m++)
614  {
615  if (is_hanging)
616  {
617  // Find the equation numbers
618  position_local_eqn_at_node = local_position_hang_eqn(
619  local_node_pt->hanging_pt()->master_node_pt(m));
620 
621  // Find the hanging node weight
622  hang_weight = local_node_pt->hanging_pt()->master_weight(m);
623  }
624  else
625  {
626  // Loop of types of dofs
627  for (unsigned k = 0; k < n_position_type; k++)
628  {
629  // Loop over the displacement components
630  for (unsigned i = 0; i < DIM; i++)
631  {
632  position_local_eqn_at_node(k, i) = position_local_eqn(l, k, i);
633  }
634  }
635 
636  // Hang weight is one
637  hang_weight = 1.0;
638  }
639 
640  // Loop over the types of dof
641  for (unsigned k = 0; k < n_position_type; k++)
642  {
643  // Loop over the directions
644  for (unsigned i = 0; i < DIM; i++)
645  {
646  // Get the equation number
647  local_eqn = position_local_eqn_at_node(k, i);
648 
649  // If not a boundary condition
650  if (local_eqn >= 0)
651  {
652  // Add the contribution
653  mass_diag[local_eqn] += pow(psi(l, k) * hang_weight, 2) * W;
654  } // End of if not boundary condition statement
655  } // End of loop over dimension
656  } // End of dof type
657  } // End of loop over master nodes
658  } // End of loop over basis functions (nodes)
659  } // End integration loop
660  }
661 
662 
663  //===========================================================================
664  /// Fill in element's contribution to the elemental
665  /// residual vector and/or Jacobian matrix.
666  /// flag=0: compute only residual vector
667  /// flag=1: compute both, fully analytically
668  /// flag=2: compute both, using FD for the derivatives w.r.t. to the
669  /// discrete displacment dofs.
670  /// flag=3: compute residuals, jacobian (full analytic) and mass matrix
671  /// flag=4: compute residuals, jacobian (FD for derivatives w.r.t.
672  /// displacements) and mass matrix
673  //==========================================================================
674  template<unsigned DIM>
677  Vector<double>& residuals,
678  DenseMatrix<double>& jacobian,
679  DenseMatrix<double>& mass_matrix,
680  const unsigned& flag)
681  {
682 #ifdef PARANOID
683  // Check if the constitutive equation requires the explicit imposition of an
684  // incompressibility constraint
686  (!this->Incompressible))
687  {
688  throw OomphLibError("The constitutive law requires the use of the "
689  "incompressible formulation by setting the element's "
690  "member function set_incompressible()",
691  OOMPH_CURRENT_FUNCTION,
692  OOMPH_EXCEPTION_LOCATION);
693  }
694 #endif
695 
696 
697  // Simply set up initial condition?
698  if (Solid_ic_pt != 0)
699  {
700  get_residuals_for_solid_ic(residuals);
701  return;
702  }
703 
704  // Find out how many nodes there are
705  const unsigned n_node = nnode();
706 
707  // Find out how many position types of dof there are
708  const unsigned n_position_type = this->nnodal_position_type();
709 
710  // Find out how many pressure dofs there are
711  const unsigned n_solid_pres = this->npres_solid();
712 
713  // Find out the index of the solid dof
714  const int solid_p_index = this->solid_p_nodal_index();
715 
716  // Local array of booleans that is true if the l-th pressure value is
717  // hanging This is an optimization because it avoids repeated virtual
718  // function calls
719  bool solid_pressure_dof_is_hanging[n_solid_pres];
720 
721  // If the solid pressure is stored at a node
722  if (solid_p_index >= 0)
723  {
724  // Read out whether the solid pressure is hanging
725  for (unsigned l = 0; l < n_solid_pres; ++l)
726  {
727  solid_pressure_dof_is_hanging[l] =
728  solid_pressure_node_pt(l)->is_hanging(solid_p_index);
729  }
730  }
731  // Otherwise the pressure is not stored at a node and so
732  // it cannot hang
733  else
734  {
735  for (unsigned l = 0; l < n_solid_pres; ++l)
736  {
737  solid_pressure_dof_is_hanging[l] = false;
738  }
739  }
740 
741  // Integer for storage of local equation and unknown numbers
742  int local_eqn = 0, local_unknown = 0;
743 
744  // Timescale ratio (non-dim density)
745  double lambda_sq = this->lambda_sq();
746 
747 
748  // Time factor
749  double time_factor = 0.0;
750  if (lambda_sq > 0)
751  {
752  time_factor = this->node_pt(0)->position_time_stepper_pt()->weight(2, 0);
753  }
754 
755 
756  // Set up memory for the shape functions
757  Shape psi(n_node, n_position_type);
758  DShape dpsidxi(n_node, n_position_type, DIM);
759 
760  // Set up memory for the pressure shape functions
761  Shape psisp(n_solid_pres);
762 
763  // Set the value of n_intpt
764  const unsigned n_intpt = integral_pt()->nweight();
765 
766  // Set the vector to hold the local coordinates in the element
767  Vector<double> s(DIM);
768 
769  // Loop over the integration points
770  for (unsigned ipt = 0; ipt < n_intpt; ipt++)
771  {
772  // Assign the values of s
773  for (unsigned i = 0; i < DIM; ++i)
774  {
775  s[i] = integral_pt()->knot(ipt, i);
776  }
777 
778  // Get the integral weight
779  double w = integral_pt()->weight(ipt);
780 
781  // Call the derivatives of the shape functions
782  double J = dshape_lagrangian_at_knot(ipt, psi, dpsidxi);
783 
784  // Call the pressure shape functions
785  this->solid_pshape_at_knot(ipt, psisp);
786 
787  // Storage for Lagrangian coordinates (initialised to zero)
788  Vector<double> interpolated_xi(DIM, 0.0);
789 
790  // Deformed tangent vectors
791  DenseMatrix<double> interpolated_G(DIM, DIM, 0.0);
792 
793  // Setup memory for accelerations
794  Vector<double> accel(DIM, 0.0);
795 
796  // Calculate displacements and derivatives and lagrangian coordinates
797  for (unsigned l = 0; l < n_node; l++)
798  {
799  // Loop over positional dofs
800  for (unsigned k = 0; k < n_position_type; k++)
801  {
802  double psi_ = psi(l, k);
803  // Loop over displacement components (deformed position)
804  for (unsigned i = 0; i < DIM; i++)
805  {
806  // Calculate the lagrangian coordinates and the accelerations
807  interpolated_xi[i] += lagrangian_position_gen(l, k, i) * psi_;
808 
809  // Only compute accelerations if inertia is switched on
810  // otherwise the timestepper might not be able to
811  // work out dx_gen_dt(2,...)
812  if ((lambda_sq > 0.0) && (this->Unsteady))
813  {
814  accel[i] += dnodal_position_gen_dt(2, l, k, i) * psi_;
815  }
816 
817  // Loop over derivative directions
818  for (unsigned j = 0; j < DIM; j++)
819  {
820  interpolated_G(j, i) +=
821  nodal_position_gen(l, k, i) * dpsidxi(l, k, j);
822  }
823  }
824  }
825  }
826 
827  // Get isotropic growth factor
828  double gamma = 1.0;
829  this->get_isotropic_growth(ipt, s, interpolated_xi, gamma);
830 
831  // Get body force at current time
832  Vector<double> b(DIM);
833  this->body_force(interpolated_xi, b);
834 
835  // We use Cartesian coordinates as the reference coordinate
836  // system. In this case the undeformed metric tensor is always
837  // the identity matrix -- stretched by the isotropic growth
838  double diag_entry = pow(gamma, 2.0 / double(DIM));
839  DenseMatrix<double> g(DIM);
840  for (unsigned i = 0; i < DIM; i++)
841  {
842  for (unsigned j = 0; j < DIM; j++)
843  {
844  if (i == j)
845  {
846  g(i, j) = diag_entry;
847  }
848  else
849  {
850  g(i, j) = 0.0;
851  }
852  }
853  }
854 
855  // Premultiply the undeformed volume ratio (from the isotropic
856  // growth), the weights and the Jacobian
857  double W = gamma * w * J;
858 
859  // Calculate the interpolated solid pressure
860  double interpolated_solid_p = 0.0;
861  for (unsigned l = 0; l < n_solid_pres; l++)
862  {
863  interpolated_solid_p += this->solid_p(l) * psisp[l];
864  }
865 
866 
867  // Declare and calculate the deformed metric tensor
868  DenseMatrix<double> G(DIM);
869 
870  // Assign values of G
871  for (unsigned i = 0; i < DIM; i++)
872  {
873  // Do upper half of matrix
874  for (unsigned j = i; j < DIM; j++)
875  {
876  // Initialise G(i,j) to zero
877  G(i, j) = 0.0;
878  // Now calculate the dot product
879  for (unsigned k = 0; k < DIM; k++)
880  {
881  G(i, j) += interpolated_G(i, k) * interpolated_G(j, k);
882  }
883  }
884  // Matrix is symmetric so just copy lower half
885  for (unsigned j = 0; j < i; j++)
886  {
887  G(i, j) = G(j, i);
888  }
889  }
890 
891  // Now calculate the deviatoric stress and all pressure-related
892  // quantitites
893  DenseMatrix<double> sigma(DIM, DIM), sigma_dev(DIM, DIM), Gup(DIM, DIM);
894  double detG = 0.0;
895  double gen_dil = 0.0;
896  double inv_kappa = 0.0;
897 
898  // Get stress derivative by FD only needed for Jacobian
899 
900  // Stress etc derivatives
901  RankFourTensor<double> d_stress_dG(DIM, DIM, DIM, DIM, 0.0);
902  // RankFourTensor<double> d_Gup_dG(DIM,DIM,DIM,DIM,0.0);
903  DenseMatrix<double> d_detG_dG(DIM, DIM, 0.0);
904  DenseMatrix<double> d_gen_dil_dG(DIM, DIM, 0.0);
905 
906  // Derivative of metric tensor w.r.t. to nodal coords
907  RankFiveTensor<double> d_G_dX(
908  n_node, n_position_type, DIM, DIM, DIM, 0.0);
909 
910  // Get Jacobian too?
911  if ((flag == 1) || (flag == 3))
912  {
913  // Derivative of metric tensor w.r.t. to discrete positional dofs
914  // NOTE: Since G is symmetric we only compute the upper triangle
915  // and DO NOT copy the entries across. Subsequent computations
916  // must (and, in fact, do) therefore only operate with upper
917  // triangular entries
918  for (unsigned ll = 0; ll < n_node; ll++)
919  {
920  for (unsigned kk = 0; kk < n_position_type; kk++)
921  {
922  for (unsigned ii = 0; ii < DIM; ii++)
923  {
924  for (unsigned aa = 0; aa < DIM; aa++)
925  {
926  for (unsigned bb = aa; bb < DIM; bb++)
927  {
928  d_G_dX(ll, kk, ii, aa, bb) =
929  interpolated_G(aa, ii) * dpsidxi(ll, kk, bb) +
930  interpolated_G(bb, ii) * dpsidxi(ll, kk, aa);
931  }
932  }
933  }
934  }
935  }
936  }
937 
938 
939  // Incompressible: Compute the deviatoric part of the stress tensor, the
940  // contravariant deformed metric tensor and the determinant
941  // of the deformed covariant metric tensor.
942  if (this->Incompressible)
943  {
944  this->get_stress(g, G, sigma_dev, Gup, detG);
945 
946  // Get full stress
947  for (unsigned a = 0; a < DIM; a++)
948  {
949  for (unsigned b = 0; b < DIM; b++)
950  {
951  sigma(a, b) = sigma_dev(a, b) - interpolated_solid_p * Gup(a, b);
952  }
953  }
954 
955  // Get Jacobian too?
956  if ((flag == 1) || (flag == 3))
957  {
958  // Get the "upper triangular" entries of the
959  // derivatives of the stress tensor with
960  // respect to G
961  this->get_d_stress_dG_upper(
962  g, G, sigma, detG, interpolated_solid_p, d_stress_dG, d_detG_dG);
963  }
964  }
965  // Nearly incompressible: Compute the deviatoric part of the
966  // stress tensor, the contravariant deformed metric tensor,
967  // the generalised dilatation and the inverse bulk modulus.
968  else
969  {
970  this->get_stress(g, G, sigma_dev, Gup, gen_dil, inv_kappa);
971 
972  // Get full stress
973  for (unsigned a = 0; a < DIM; a++)
974  {
975  for (unsigned b = 0; b < DIM; b++)
976  {
977  sigma(a, b) = sigma_dev(a, b) - interpolated_solid_p * Gup(a, b);
978  }
979  }
980 
981  // Get Jacobian too?
982  if ((flag == 1) || (flag == 3))
983  {
984  // Get the "upper triangular" entries of the derivatives
985  // of the stress tensor with
986  // respect to G
987  this->get_d_stress_dG_upper(g,
988  G,
989  sigma,
990  gen_dil,
991  inv_kappa,
992  interpolated_solid_p,
993  d_stress_dG,
994  d_gen_dil_dG);
995  }
996  }
997 
998  // Add pre-stress
999  for (unsigned i = 0; i < DIM; i++)
1000  {
1001  for (unsigned j = 0; j < DIM; j++)
1002  {
1003  sigma(i, j) += this->prestress(i, j, interpolated_xi);
1004  }
1005  }
1006 
1007  //=====EQUATIONS OF ELASTICITY FROM PRINCIPLE OF VIRTUAL
1008  // DISPLACEMENTS========
1009 
1010  unsigned n_master = 1;
1011  double hang_weight = 1.0;
1012 
1013  // Loop over the test functions, nodes of the element
1014  for (unsigned l = 0; l < n_node; l++)
1015  {
1016  // Get pointer to local node l
1017  Node* local_node_pt = node_pt(l);
1018 
1019  // Cache hang status
1020  bool is_hanging = local_node_pt->is_hanging();
1021 
1022  // If the node is a hanging node
1023  if (is_hanging)
1024  {
1025  n_master = local_node_pt->hanging_pt()->nmaster();
1026  }
1027  // Otherwise the node is its own master
1028  else
1029  {
1030  n_master = 1;
1031  }
1032 
1033 
1034  // Storage for local equation numbers at node indexed by
1035  // type and direction
1036  DenseMatrix<int> position_local_eqn_at_node(n_position_type, DIM);
1037 
1038  // Loop over the master nodes
1039  for (unsigned m = 0; m < n_master; m++)
1040  {
1041  if (is_hanging)
1042  {
1043  // Find the equation numbers
1044  position_local_eqn_at_node = local_position_hang_eqn(
1045  local_node_pt->hanging_pt()->master_node_pt(m));
1046 
1047  // Find the hanging node weight
1048  hang_weight = local_node_pt->hanging_pt()->master_weight(m);
1049  }
1050  else
1051  {
1052  // Loop of types of dofs
1053  for (unsigned k = 0; k < n_position_type; k++)
1054  {
1055  // Loop over the displacement components
1056  for (unsigned i = 0; i < DIM; i++)
1057  {
1058  position_local_eqn_at_node(k, i) = position_local_eqn(l, k, i);
1059  }
1060  }
1061 
1062  // Hang weight is one
1063  hang_weight = 1.0;
1064  }
1065 
1066 
1067  // Loop of types of dofs
1068  for (unsigned k = 0; k < n_position_type; k++)
1069  {
1070  // Offset for faster access
1071  const unsigned offset5 = dpsidxi.offset(l, k);
1072 
1073  // Loop over the displacement components
1074  for (unsigned i = 0; i < DIM; i++)
1075  {
1076  local_eqn = position_local_eqn_at_node(k, i);
1077 
1078  /*IF it's not a boundary condition*/
1079  if (local_eqn >= 0)
1080  {
1081  // Initialise contribution to zero
1082  double sum = 0.0;
1083 
1084  // Acceleration and body force
1085  sum += (lambda_sq * accel[i] - b[i]) * psi(l, k);
1086 
1087  // Stress term
1088  for (unsigned a = 0; a < DIM; a++)
1089  {
1090  unsigned count = offset5;
1091  for (unsigned b = 0; b < DIM; b++)
1092  {
1093  // Add the stress terms to the residuals
1094  sum += sigma(a, b) * interpolated_G(a, i) *
1095  dpsidxi.raw_direct_access(count);
1096  ++count;
1097  }
1098  }
1099  residuals[local_eqn] += W * sum * hang_weight;
1100 
1101 
1102  // Get the mass matrix
1103  // This involves another loop over the points
1104  // because the jacobian may NOT be being calculated analytically
1105  // It could be made more efficient in th event that
1106  // we eventually decide not (never) to
1107  // use finite differences.
1108  if (flag > 2)
1109  {
1110  // Default setting for non-hanging node
1111  unsigned nn_master = 1;
1112  double hhang_weight = 1.0;
1113 
1114  // Loop over the nodes of the element again
1115  for (unsigned ll = 0; ll < n_node; ll++)
1116  {
1117  // Get pointer to local node ll
1118  Node* llocal_node_pt = node_pt(ll);
1119 
1120  // Cache hang status
1121  bool iis_hanging = llocal_node_pt->is_hanging();
1122 
1123  // If the node is a hanging node
1124  if (iis_hanging)
1125  {
1126  nn_master = llocal_node_pt->hanging_pt()->nmaster();
1127  }
1128  // Otherwise the node is its own master
1129  else
1130  {
1131  nn_master = 1;
1132  }
1133 
1134 
1135  // Storage for local unknown numbers at node indexed by
1136  // type and direction
1137  DenseMatrix<int> position_local_unk_at_node(n_position_type,
1138  DIM);
1139 
1140  // Loop over the master nodes
1141  for (unsigned mm = 0; mm < nn_master; mm++)
1142  {
1143  if (iis_hanging)
1144  {
1145  // Find the unknown numbers
1146  position_local_unk_at_node = local_position_hang_eqn(
1147  llocal_node_pt->hanging_pt()->master_node_pt(mm));
1148 
1149  // Find the hanging node weight
1150  hhang_weight =
1151  llocal_node_pt->hanging_pt()->master_weight(mm);
1152  }
1153  else
1154  {
1155  // Loop of types of dofs
1156  for (unsigned kk = 0; kk < n_position_type; kk++)
1157  {
1158  // Loop over the displacement components
1159  for (unsigned ii = 0; ii < DIM; ii++)
1160  {
1161  position_local_unk_at_node(kk, ii) =
1162  position_local_eqn(ll, kk, ii);
1163  }
1164  }
1165 
1166  // Hang weight is one
1167  hhang_weight = 1.0;
1168  }
1169 
1170 
1171  // Loop of types of dofs again
1172  for (unsigned kk = 0; kk < n_position_type; kk++)
1173  {
1174  // Get the number of the unknown
1175  int local_unknown = position_local_unk_at_node(kk, i);
1176 
1177  /*IF it's not a boundary condition*/
1178  if (local_unknown >= 0)
1179  {
1180  mass_matrix(local_eqn, local_unknown) +=
1181  lambda_sq * psi(l, k) * psi(ll, kk) * hang_weight *
1182  hhang_weight * W;
1183  }
1184  }
1185  }
1186  }
1187  }
1188 
1189 
1190  // Get Jacobian too?
1191  if ((flag == 1) || (flag == 3))
1192  {
1193  // Offset for faster access in general stress loop
1194  const unsigned offset1 = d_G_dX.offset(l, k, i);
1195 
1196  // Default setting for non-hanging node
1197  unsigned nn_master = 1;
1198  double hhang_weight = 1.0;
1199 
1200  // Loop over the nodes of the element again
1201  for (unsigned ll = 0; ll < n_node; ll++)
1202  {
1203  // Get pointer to local node ll
1204  Node* llocal_node_pt = node_pt(ll);
1205 
1206  // Cache hang status
1207  bool iis_hanging = llocal_node_pt->is_hanging();
1208 
1209  // If the node is a hanging node
1210  if (iis_hanging)
1211  {
1212  nn_master = llocal_node_pt->hanging_pt()->nmaster();
1213  }
1214  // Otherwise the node is its own master
1215  else
1216  {
1217  nn_master = 1;
1218  }
1219 
1220 
1221  // Storage for local unknown numbers at node indexed by
1222  // type and direction
1223  DenseMatrix<int> position_local_unk_at_node(n_position_type,
1224  DIM);
1225 
1226  // Loop over the master nodes
1227  for (unsigned mm = 0; mm < nn_master; mm++)
1228  {
1229  if (iis_hanging)
1230  {
1231  // Find the unknown numbers
1232  position_local_unk_at_node = local_position_hang_eqn(
1233  llocal_node_pt->hanging_pt()->master_node_pt(mm));
1234 
1235  // Find the hanging node weight
1236  hhang_weight =
1237  llocal_node_pt->hanging_pt()->master_weight(mm);
1238  }
1239  else
1240  {
1241  // Loop of types of dofs
1242  for (unsigned kk = 0; kk < n_position_type; kk++)
1243  {
1244  // Loop over the displacement components
1245  for (unsigned ii = 0; ii < DIM; ii++)
1246  {
1247  position_local_unk_at_node(kk, ii) =
1248  position_local_eqn(ll, kk, ii);
1249  }
1250  }
1251 
1252  // Hang weight is one
1253  hhang_weight = 1.0;
1254  }
1255 
1256 
1257  // Loop of types of dofs again
1258  for (unsigned kk = 0; kk < n_position_type; kk++)
1259  {
1260  // Loop over the displacement components again
1261  for (unsigned ii = 0; ii < DIM; ii++)
1262  {
1263  // Get the number of the unknown
1264  int local_unknown =
1265  position_local_unk_at_node(kk, ii);
1266 
1267  /*IF it's not a boundary condition*/
1268  if (local_unknown >= 0)
1269  {
1270  // Offset for faster access in general stress loop
1271  const unsigned offset2 = d_G_dX.offset(ll, kk, ii);
1272  const unsigned offset4 = dpsidxi.offset(ll, kk);
1273 
1274 
1275  // General stress term
1276  //--------------------
1277  double sum = 0.0;
1278  unsigned count1 = offset1;
1279  for (unsigned a = 0; a < DIM; a++)
1280  {
1281  // Bump up direct access because we're only
1282  // accessing upper triangle
1283  count1 += a;
1284  for (unsigned b = a; b < DIM; b++)
1285  {
1286  double factor =
1287  d_G_dX.raw_direct_access(count1);
1288  if (a == b) factor *= 0.5;
1289 
1290  // Offset for faster access
1291  unsigned offset3 = d_stress_dG.offset(a, b);
1292  unsigned count2 = offset2;
1293  unsigned count3 = offset3;
1294 
1295  for (unsigned aa = 0; aa < DIM; aa++)
1296  {
1297  // Bump up direct access because we're only
1298  // accessing upper triangle
1299  count2 += aa;
1300  count3 += aa;
1301 
1302  // Only upper half of derivatives w.r.t.
1303  // symm tensor
1304  for (unsigned bb = aa; bb < DIM; bb++)
1305  {
1306  sum +=
1307  factor *
1308  d_stress_dG.raw_direct_access(count3) *
1309  d_G_dX.raw_direct_access(count2);
1310  ++count2;
1311  ++count3;
1312  }
1313  }
1314  ++count1;
1315  }
1316  }
1317 
1318  // Multiply by weight and add contribution
1319  // (Add directly because this bit is nonsymmetric)
1320  jacobian(local_eqn, local_unknown) +=
1321  sum * W * hang_weight * hhang_weight;
1322 
1323  // Only upper triangle (no separate test for bc as
1324  // local_eqn is already nonnegative)
1325  if ((i == ii) && (local_unknown >= local_eqn))
1326  {
1327  // Initialise contribution
1328  double sum = 0.0;
1329 
1330  // Inertia term
1331  sum += lambda_sq * time_factor * psi(ll, kk) *
1332  psi(l, k);
1333 
1334  // Stress term
1335  unsigned count4 = offset4;
1336  for (unsigned a = 0; a < DIM; a++)
1337  {
1338  // Cache term
1339  const double factor =
1340  dpsidxi.raw_direct_access(count4); // ll ,kk
1341  ++count4;
1342 
1343  unsigned count5 = offset5;
1344  for (unsigned b = 0; b < DIM; b++)
1345  {
1346  sum +=
1347  sigma(a, b) * factor *
1348  dpsidxi.raw_direct_access(count5); // l ,k
1349  ++count5;
1350  }
1351  }
1352 
1353  // Multiply by weights to form contribution
1354  double sym_entry =
1355  sum * W * hang_weight * hhang_weight;
1356  // Add contribution to jacobian
1357  jacobian(local_eqn, local_unknown) += sym_entry;
1358  // Add to lower triangular entries
1359  if (local_eqn != local_unknown)
1360  {
1361  jacobian(local_unknown, local_eqn) += sym_entry;
1362  }
1363  }
1364  } // End of if not boundary condition
1365  }
1366  }
1367  }
1368  }
1369  }
1370 
1371  // Can add in the pressure jacobian terms
1372  if (flag > 0)
1373  {
1374  // Loop over the pressure nodes
1375  for (unsigned l2 = 0; l2 < n_solid_pres; l2++)
1376  {
1377  unsigned n_master2 = 1;
1378  double hang_weight2 = 1.0;
1379  HangInfo* hang_info2_pt = 0;
1380 
1381  bool is_hanging2 = solid_pressure_dof_is_hanging[l2];
1382  if (is_hanging2)
1383  {
1384  // Get the HangInfo object associated with the
1385  // hanging solid pressure
1386  hang_info2_pt =
1387  solid_pressure_node_pt(l2)->hanging_pt(solid_p_index);
1388 
1389  n_master2 = hang_info2_pt->nmaster();
1390  }
1391  else
1392  {
1393  n_master2 = 1;
1394  }
1395 
1396  // Loop over all the master nodes
1397  for (unsigned m2 = 0; m2 < n_master2; m2++)
1398  {
1399  if (is_hanging2)
1400  {
1401  // Get the equation numbers at the master node
1402  local_unknown = local_hang_eqn(
1403  hang_info2_pt->master_node_pt(m2), solid_p_index);
1404 
1405  // Find the hanging node weight at the node
1406  hang_weight2 = hang_info2_pt->master_weight(m2);
1407  }
1408  else
1409  {
1410  local_unknown = this->solid_p_local_eqn(l2);
1411  hang_weight2 = 1.0;
1412  }
1413 
1414  // If it's not a boundary condition
1415  if (local_unknown >= 0)
1416  {
1417  // Add the pressure terms to the jacobian
1418  for (unsigned a = 0; a < DIM; a++)
1419  {
1420  for (unsigned b = 0; b < DIM; b++)
1421  {
1422  jacobian(local_eqn, local_unknown) -=
1423  psisp[l2] * Gup(a, b) * interpolated_G(a, i) *
1424  dpsidxi(l, k, b) * W * hang_weight * hang_weight2;
1425  }
1426  }
1427  }
1428  } // End of loop over master nodes
1429  } // End of loop over pressure dofs
1430  } // End of Jacobian terms
1431 
1432  } // End of if not boundary condition
1433  }
1434  }
1435  } // End of loop of over master nodes
1436 
1437  } // End of loop over nodes
1438 
1439  //==============CONSTRAINT EQUATIONS FOR PRESSURE=====================
1440 
1441  // Now loop over the pressure degrees of freedom
1442  for (unsigned l = 0; l < n_solid_pres; l++)
1443  {
1444  bool is_hanging = solid_pressure_dof_is_hanging[l];
1445 
1446  unsigned n_master = 1;
1447  double hang_weight = 1.0;
1448  HangInfo* hang_info_pt = 0;
1449 
1450  // If the node is a hanging node
1451  if (is_hanging)
1452  {
1453  // Get a pointer to the HangInfo object associated with the
1454  // solid pressure (stored at solid_p_index)
1455  hang_info_pt = solid_pressure_node_pt(l)->hanging_pt(solid_p_index);
1456 
1457  // Number of master nodes
1458  n_master = hang_info_pt->nmaster();
1459  }
1460  // Otherwise the node is its own master
1461  else
1462  {
1463  n_master = 1;
1464  }
1465 
1466  // Loop over all the master nodes
1467  // Note that the pressure is stored at the inded solid_p_index
1468  for (unsigned m = 0; m < n_master; m++)
1469  {
1470  if (is_hanging)
1471  {
1472  // Get the equation numbers at the master node
1473  local_eqn =
1474  local_hang_eqn(hang_info_pt->master_node_pt(m), solid_p_index);
1475 
1476  // Find the hanging node weight at the node
1477  hang_weight = hang_info_pt->master_weight(m);
1478  }
1479  else
1480  {
1481  local_eqn = this->solid_p_local_eqn(l);
1482  }
1483 
1484  // Pinned (unlikely, actually) or real dof?
1485  if (local_eqn >= 0)
1486  {
1487  // For true incompressibility we need to conserve volume
1488  // so the determinant of the deformed metric tensor
1489  // needs to be equal to that of the undeformed one, which
1490  // is equal to the volumetric growth factor
1491  if (this->Incompressible)
1492  {
1493  residuals[local_eqn] +=
1494  (detG - gamma) * psisp[l] * W * hang_weight;
1495 
1496  // Get Jacobian too?
1497  if ((flag == 1) || (flag == 3))
1498  {
1499  // Default setting for non-hanging node
1500  unsigned nn_master = 1;
1501  double hhang_weight = 1.0;
1502 
1503  // Loop over the nodes of the element again
1504  for (unsigned ll = 0; ll < n_node; ll++)
1505  {
1506  // Get pointer to local node ll
1507  Node* llocal_node_pt = node_pt(ll);
1508 
1509  // Cache hang status
1510  bool iis_hanging = llocal_node_pt->is_hanging();
1511 
1512  // If the node is a hanging node
1513  if (iis_hanging)
1514  {
1515  nn_master = llocal_node_pt->hanging_pt()->nmaster();
1516  }
1517  // Otherwise the node is its own master
1518  else
1519  {
1520  nn_master = 1;
1521  }
1522 
1523  // Storage for local unknown numbers at node indexed by
1524  // type and direction
1525  DenseMatrix<int> position_local_unk_at_node(n_position_type,
1526  DIM);
1527 
1528  // Loop over the master nodes
1529  for (unsigned mm = 0; mm < nn_master; mm++)
1530  {
1531  if (iis_hanging)
1532  {
1533  // Find the unknown numbers
1534  position_local_unk_at_node = local_position_hang_eqn(
1535  llocal_node_pt->hanging_pt()->master_node_pt(mm));
1536 
1537  // Find the hanging node weight
1538  hhang_weight =
1539  llocal_node_pt->hanging_pt()->master_weight(mm);
1540  }
1541  else
1542  {
1543  // Loop of types of dofs
1544  for (unsigned kk = 0; kk < n_position_type; kk++)
1545  {
1546  // Loop over the displacement components
1547  for (unsigned ii = 0; ii < DIM; ii++)
1548  {
1549  position_local_unk_at_node(kk, ii) =
1550  position_local_eqn(ll, kk, ii);
1551  }
1552  }
1553 
1554  // Hang weight is one
1555  hhang_weight = 1.0;
1556  }
1557 
1558 
1559  // Loop of types of dofs again
1560  for (unsigned kk = 0; kk < n_position_type; kk++)
1561  {
1562  // Loop over the displacement components again
1563  for (unsigned ii = 0; ii < DIM; ii++)
1564  {
1565  // Get the number of the unknown
1566  int local_unknown = position_local_unk_at_node(kk, ii);
1567 
1568  /*IF it's not a boundary condition*/
1569  if (local_unknown >= 0)
1570  {
1571  // Offset for faster access
1572  const unsigned offset = d_G_dX.offset(ll, kk, ii);
1573 
1574  // General stress term
1575  double sum = 0.0;
1576  unsigned count = offset;
1577  for (unsigned aa = 0; aa < DIM; aa++)
1578  {
1579  // Bump up direct access because we're only
1580  // accessing upper triangle
1581  count += aa;
1582 
1583  // Only upper half
1584  for (unsigned bb = aa; bb < DIM; bb++)
1585  {
1586  sum += d_detG_dG(aa, bb) *
1587  d_G_dX.raw_direct_access(count) * psisp(l);
1588  ++count;
1589  }
1590  }
1591  jacobian(local_eqn, local_unknown) +=
1592  sum * W * hang_weight * hhang_weight;
1593  }
1594  }
1595  }
1596  }
1597  }
1598 
1599  // No Jacobian terms due to pressure since it does not feature
1600  // in the incompressibility constraint
1601  }
1602  }
1603  // Nearly incompressible: (Neg.) pressure given by product of
1604  // bulk modulus and generalised dilatation
1605  else
1606  {
1607  residuals[local_eqn] +=
1608  (inv_kappa * interpolated_solid_p + gen_dil) * psisp[l] * W *
1609  hang_weight;
1610 
1611  // Add in the jacobian terms
1612  if ((flag == 1) || (flag == 3))
1613  {
1614  // Default setting for non-hanging node
1615  unsigned nn_master = 1;
1616  double hhang_weight = 1.0;
1617 
1618  // Loop over the nodes of the element again
1619  for (unsigned ll = 0; ll < n_node; ll++)
1620  {
1621  // Get pointer to local node ll
1622  Node* llocal_node_pt = node_pt(ll);
1623 
1624  // Cache hang status
1625  bool iis_hanging = llocal_node_pt->is_hanging();
1626 
1627  // If the node is a hanging node
1628  if (iis_hanging)
1629  {
1630  nn_master = llocal_node_pt->hanging_pt()->nmaster();
1631  }
1632  // Otherwise the node is its own master
1633  else
1634  {
1635  nn_master = 1;
1636  }
1637 
1638 
1639  // Storage for local unknown numbers at node indexed by
1640  // type and direction
1641  DenseMatrix<int> position_local_unk_at_node(n_position_type,
1642  DIM);
1643 
1644  // Loop over the master nodes
1645  for (unsigned mm = 0; mm < nn_master; mm++)
1646  {
1647  if (iis_hanging)
1648  {
1649  // Find the unknown numbers
1650  position_local_unk_at_node = local_position_hang_eqn(
1651  llocal_node_pt->hanging_pt()->master_node_pt(mm));
1652 
1653  // Find the hanging node weight
1654  hhang_weight =
1655  llocal_node_pt->hanging_pt()->master_weight(mm);
1656  }
1657  else
1658  {
1659  // Loop of types of dofs
1660  for (unsigned kk = 0; kk < n_position_type; kk++)
1661  {
1662  // Loop over the displacement components
1663  for (unsigned ii = 0; ii < DIM; ii++)
1664  {
1665  position_local_unk_at_node(kk, ii) =
1666  position_local_eqn(ll, kk, ii);
1667  }
1668  }
1669 
1670  // Hang weight is one
1671  hhang_weight = 1.0;
1672  }
1673 
1674 
1675  // Loop of types of dofs again
1676  for (unsigned kk = 0; kk < n_position_type; kk++)
1677  {
1678  // Loop over the displacement components again
1679  for (unsigned ii = 0; ii < DIM; ii++)
1680  {
1681  // Get the number of the unknown
1682  int local_unknown = position_local_unk_at_node(kk, ii);
1683 
1684  /*IF it's not a boundary condition*/
1685  if (local_unknown >= 0)
1686  {
1687  // Offset for faster access
1688  const unsigned offset = d_G_dX.offset(ll, kk, ii);
1689 
1690  // General stress term
1691  double sum = 0.0;
1692  unsigned count = offset;
1693  for (unsigned aa = 0; aa < DIM; aa++)
1694  {
1695  // Bump up direct access because we're only
1696  // accessing upper triangle
1697  count += aa;
1698 
1699  // Only upper half
1700  for (unsigned bb = aa; bb < DIM; bb++)
1701  {
1702  sum += d_gen_dil_dG(aa, bb) *
1703  d_G_dX.raw_direct_access(count) * psisp(l);
1704  ++count;
1705  }
1706  }
1707  jacobian(local_eqn, local_unknown) +=
1708  sum * W * hang_weight * hhang_weight;
1709  }
1710  }
1711  }
1712  }
1713  }
1714  }
1715 
1716 
1717  // Add in the pressure jacobian terms
1718  if (flag > 0)
1719  {
1720  // Loop over the pressure nodes again
1721  for (unsigned l2 = 0; l2 < n_solid_pres; l2++)
1722  {
1723  bool is_hanging2 = solid_pressure_dof_is_hanging[l2];
1724 
1725  unsigned n_master2 = 1;
1726  double hang_weight2 = 1.0;
1727  HangInfo* hang_info2_pt = 0;
1728 
1729  if (is_hanging2)
1730  {
1731  // Get pointer to hang info object
1732  // Note that the pressure is stored at
1733  // the index solid_p_index
1734  hang_info2_pt =
1735  solid_pressure_node_pt(l2)->hanging_pt(solid_p_index);
1736 
1737  n_master2 = hang_info2_pt->nmaster();
1738  }
1739  else
1740  {
1741  n_master2 = 1;
1742  }
1743 
1744  // Loop over all the master nodes
1745  for (unsigned m2 = 0; m2 < n_master2; m2++)
1746  {
1747  if (is_hanging2)
1748  {
1749  // Get the equation numbers at the master node
1750  local_unknown = local_hang_eqn(
1751  hang_info2_pt->master_node_pt(m2), solid_p_index);
1752 
1753  // Find the hanging node weight at the node
1754  hang_weight2 = hang_info2_pt->master_weight(m2);
1755  }
1756  else
1757  {
1758  local_unknown = this->solid_p_local_eqn(l2);
1759  hang_weight2 = 1.0;
1760  }
1761 
1762  // If it's not a boundary condition
1763  if (local_unknown >= 0)
1764  {
1765  jacobian(local_eqn, local_unknown) +=
1766  inv_kappa * psisp[l2] * psisp[l] * W * hang_weight *
1767  hang_weight2;
1768  }
1769 
1770  } // End of loop over master nodes
1771  } // End of loop over pressure dofs
1772  } // End of pressure Jacobian
1773 
1774 
1775  } // End of nearly incompressible case
1776  } // End of if not boundary condition
1777  } // End of loop over master nodes
1778  } // End of loop over pressure dofs
1779  } // End of loop over integration points
1780  }
1781 
1782 
1783  //====================================================================
1784  /// Forcing building of required templates
1785  //====================================================================
1786  template class RefineablePVDEquations<2>;
1787  template class RefineablePVDEquations<3>;
1788 
1791 
1792 } // namespace oomph
static char t char * s
Definition: cfortran.h:568
cstr elem_len * i
Definition: cfortran.h:603
virtual bool requires_incompressibility_constraint()=0
Pure virtual function in which the user must declare if the constitutive equation requires an incompr...
A Class for the derivatives of shape functions The class design is essentially the same as Shape,...
Definition: shape.h:278
unsigned offset(const unsigned long &i, const unsigned long &j) const
Caculate the offset in flat-packed C-style, column-major format, required for a given i,...
Definition: shape.h:487
double & raw_direct_access(const unsigned long &i)
Direct access to internal storage of data in flat-packed C-style column-major format....
Definition: shape.h:469
Class that contains data for hanging nodes.
Definition: nodes.h:742
double const & master_weight(const unsigned &i) const
Return weight for dofs on i-th master node.
Definition: nodes.h:808
Node *const & master_node_pt(const unsigned &i) const
Return a pointer to the i-th master node.
Definition: nodes.h:791
unsigned nmaster() const
Return the number of master nodes.
Definition: nodes.h:785
Nodes are derived from Data, but, in addition, have a definite (Eulerian) position in a space of a gi...
Definition: nodes.h:906
HangInfo *const & hanging_pt() const
Return pointer to hanging node data (this refers to the geometric hanging node status) (const version...
Definition: nodes.h:1228
bool is_hanging() const
Test whether the node is geometrically hanging.
Definition: nodes.h:1285
An OomphLibError object which should be thrown when an run-time error is encountered....
/////////////////////////////////////////////////////////////// /////////////////////////////////////...
Definition: matrices.h:2113
T & raw_direct_access(const unsigned long &i)
Direct access to internal storage of data in flat-packed C-style column-major format....
Definition: matrices.h:2545
unsigned offset(const unsigned long &i, const unsigned long &j, const unsigned long &k) const
Caculate the offset in flat-packed Cy-style, column-major format, required for a given i,...
Definition: matrices.h:2564
////////////////////////////////////////////////////////////////// //////////////////////////////////...
Definition: matrices.h:1701
T & raw_direct_access(const unsigned long &i)
Direct access to internal storage of data in flat-packed C-style column-major format....
Definition: matrices.h:2078
unsigned offset(const unsigned long &i, const unsigned long &j) const
Caculate the offset in flat-packed C-style, column-major format, required for a given i,...
Definition: matrices.h:2096
Class for Refineable solid mechanics elements in near-incompressible/ incompressible formulation,...
void fill_in_generic_residual_contribution_pvd_with_pressure(Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, const unsigned &flag)
Add element's contribution to elemental residual vector and/or Jacobian matrix flag=1: compute both f...
void get_mass_matrix_diagonal(Vector< double > &mass_diag)
Compute the diagonal of the displacement mass matrix for LSC preconditioner.
Class for Refineable PVD equations.
void fill_in_generic_contribution_to_residuals_pvd(Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)
Call the residuals including hanging node cases.
A Class for shape functions. In simple cases, the shape functions have only one index that can be tho...
Definition: shape.h:76
ConstitutiveLaw * Constitutive_law_pt
Create constitutive law (for smoothing by nonlinear elasticity)
Definition: mesh_smooth.h:55
//////////////////////////////////////////////////////////////////// ////////////////////////////////...