GetFEM  5.4.3
getfem_global_function.h
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32 
33 /**@file getfem_global_function.h
34  @author Yves Renard <Yves.Renard@insa-lyon.fr>, J. Pommier
35  @date March, 2005.
36  @brief Definition of global functions to be used as base or enrichment
37  functions in fem.
38 */
39 #ifndef GETFEM_GLOBAL_FUNCTION_H__
40 #define GETFEM_GLOBAL_FUNCTION_H__
41 
42 #include "bgeot_rtree.h"
43 #include "getfem_mesh_fem.h"
44 #include "getfem_generic_assembly.h"
45 
46 namespace getfem {
47 
48  /// inherit from this class to define new global functions.
49  class global_function : virtual public dal::static_stored_object {
50  protected:
51  const dim_type dim_;
52  public:
53  dim_type dim() const { return dim_; }
54 
55  virtual scalar_type val(const fem_interpolation_context&) const
56  { GMM_ASSERT1(false, "this global_function has no value"); }
57  virtual void grad(const fem_interpolation_context&, base_small_vector&) const
58  { GMM_ASSERT1(false, "this global_function has no gradient"); }
59  virtual void hess(const fem_interpolation_context&, base_matrix&) const
60  { GMM_ASSERT1(false, "this global_function has no hessian"); }
61 
62  virtual bool is_in_support(const base_node & /* pt */ ) const { return true; }
63  virtual void bounding_box(base_node &bmin, base_node &bmax) const {
64  GMM_ASSERT1(bmin.size() == dim_ && bmax.size() == dim_,
65  "Wrong dimensions");
66  for (auto&& xx : bmin) xx = -1e+25;
67  for (auto&& xx : bmax) xx = 1e+25;
68  }
69 
70  global_function(dim_type dim__) : dim_(dim__)
71  { DAL_STORED_OBJECT_DEBUG_CREATED(this, "Global function");}
72  virtual ~global_function()
73  { DAL_STORED_OBJECT_DEBUG_DESTROYED(this, "Global function"); }
74  };
75 
76  typedef std::shared_ptr<const global_function> pglobal_function;
77 
78 
79  class global_function_simple : public global_function {
80  public:
81  // These virtual functions can not be further overriden in derived classes
82  virtual scalar_type val(const fem_interpolation_context&) const final;
83  virtual void grad(const fem_interpolation_context&, base_small_vector&) const final;
84  virtual void hess(const fem_interpolation_context&, base_matrix&) const final;
85  // You have to override these instead
86  virtual scalar_type val(const base_node &pt) const = 0;
87  virtual void grad(const base_node &pt, base_small_vector&) const = 0;
88  virtual void hess(const base_node &pt, base_matrix&) const = 0;
89 
90  global_function_simple(dim_type dim__) : global_function(dim__)
91  { DAL_STORED_OBJECT_DEBUG_CREATED(this, "Global function simple"); }
92  virtual ~global_function_simple()
93  { DAL_STORED_OBJECT_DEBUG_DESTROYED(this, "Global function simple"); }
94  };
95 
96  class global_function_parser : public global_function_simple {
97  ga_workspace gw;
98  ga_function f_val, f_grad, f_hess;
99  mutable model_real_plain_vector pt_;
100  public:
101  virtual scalar_type val(const base_node &pt) const;
102  virtual const base_tensor &tensor_val(const base_node &pt) const;
103  virtual void grad(const base_node &pt, base_small_vector &g) const;
104  virtual void hess(const base_node &pt, base_matrix &h) const;
105 
106  global_function_parser(dim_type dim_,
107  const std::string &sval,
108  const std::string &sgrad="",
109  const std::string &shess="");
110  virtual ~global_function_parser()
111  { DAL_STORED_OBJECT_DEBUG_DESTROYED(this, "Global function parser"); }
112  };
113 
114 
115  class global_function_sum : public global_function {
116  std::vector<pglobal_function> functions;
117  public:
118  virtual scalar_type val(const fem_interpolation_context&) const;
119  virtual void grad(const fem_interpolation_context&, base_small_vector&) const;
120  virtual void hess(const fem_interpolation_context&, base_matrix&) const;
121  virtual bool is_in_support(const base_node &p) const;
122  virtual void bounding_box(base_node &bmin_, base_node &bmax_) const;
123  global_function_sum(const std::vector<pglobal_function> &funcs);
124  global_function_sum(pglobal_function f1, pglobal_function f2);
125  global_function_sum(pglobal_function f1, pglobal_function f2,
126  pglobal_function f3);
127  global_function_sum(pglobal_function f1, pglobal_function f2,
128  pglobal_function f3, pglobal_function f4);
129  virtual ~global_function_sum()
130  { DAL_STORED_OBJECT_DEBUG_DESTROYED(this, "Global function sum"); }
131  };
132 
133  class global_function_product : public global_function {
134  pglobal_function f1, f2;
135  public:
136  virtual scalar_type val(const fem_interpolation_context&) const;
137  virtual void grad(const fem_interpolation_context&, base_small_vector&) const;
138  virtual void hess(const fem_interpolation_context&, base_matrix&) const;
139  virtual bool is_in_support(const base_node &p) const;
140  virtual void bounding_box(base_node &bmin_, base_node &bmax_) const;
141  global_function_product(pglobal_function f1_, pglobal_function f2_);
142  virtual ~global_function_product()
143  { DAL_STORED_OBJECT_DEBUG_DESTROYED(this, "Global function product"); }
144  };
145 
146  class global_function_bounded : public global_function {
147  pglobal_function f;
148  const base_node bmin, bmax;
149  bool has_expr;
150  ga_workspace gw;
151  ga_function f_val;
152  mutable model_real_plain_vector pt_;
153  public:
154  virtual scalar_type val(const fem_interpolation_context &c) const
155  { return f->val(c); }
156  virtual void grad(const fem_interpolation_context &c, base_small_vector &g) const
157  { f->grad(c, g); }
158  virtual void hess(const fem_interpolation_context &c, base_matrix &h) const
159  { f->hess(c, h); }
160 
161  virtual bool is_in_support(const base_node &) const;
162  virtual void bounding_box(base_node &bmin_, base_node &bmax_) const {
163  bmin_ = bmin;
164  bmax_ = bmax;
165  }
166  // is_in_expr should evaluate to a positive result inside the support of the
167  // function and negative elsewhere
168  global_function_bounded(pglobal_function f_,
169  const base_node &bmin_, const base_node &bmax_,
170  const std::string &is_in_expr="");
171  virtual ~global_function_bounded()
172  { DAL_STORED_OBJECT_DEBUG_DESTROYED(this, "Global function bounded"); }
173  };
174 
175 
176  /** a general structure for interpolation of a function defined
177  by a mesh_fem and a vector U at any point
178  (interpolation of value and gradient).
179  */
180 
181  struct interpolator_on_mesh_fem {
182  const mesh_fem &mf;
183  std::vector<scalar_type> U;
184 
185  mutable bgeot::rtree boxtree;
186  mutable size_type cv_stored;
187  mutable bgeot::rtree::pbox_set boxlst;
188  mutable bgeot::geotrans_inv_convex gic;
189 
190 
191  interpolator_on_mesh_fem(const mesh_fem &mf_,
192  const std::vector<scalar_type> &U_);
193  bool find_a_point(const base_node &pt, base_node &ptr,
194  size_type &cv) const;
195  bool eval(const base_node &pt, base_vector &val, base_matrix &grad) const;
196  };
197 
198  typedef std::shared_ptr<const interpolator_on_mesh_fem>
199  pinterpolator_on_mesh_fem;
200 
201 
202  /** below a list of simple functions of (x,y)
203  used for building the crack singular functions
204  */
205  class abstract_xy_function : virtual public dal::static_stored_object {
206  public:
207  virtual scalar_type val(scalar_type x, scalar_type y) const = 0;
208  virtual base_small_vector grad(scalar_type x, scalar_type y) const = 0;
209  virtual base_matrix hess(scalar_type x, scalar_type y) const = 0;
210  virtual ~abstract_xy_function() {}
211  };
212 
213  typedef std::shared_ptr<const abstract_xy_function> pxy_function;
214 
215  struct parser_xy_function : public abstract_xy_function {
216  ga_workspace gw;
217  ga_function f_val, f_grad, f_hess;
218  mutable model_real_plain_vector ptx, pty, ptr, ptt;
219 
220  virtual scalar_type val(scalar_type x, scalar_type y) const;
221  virtual base_small_vector grad(scalar_type x, scalar_type y) const;
222  virtual base_matrix hess(scalar_type x, scalar_type y) const;
223 
224  parser_xy_function(const std::string &sval,
225  const std::string &sgrad="0;0;",
226  const std::string &shess="0;0;0;0;");
227  virtual ~parser_xy_function() {}
228  };
229 
230  struct crack_singular_xy_function : public abstract_xy_function {
231  unsigned l; /* 0 <= l <= 6 */
232  virtual scalar_type val(scalar_type x, scalar_type y) const;
233  virtual base_small_vector grad(scalar_type x, scalar_type y) const;
234  virtual base_matrix hess(scalar_type x, scalar_type y) const;
235  crack_singular_xy_function(unsigned l_) : l(l_) {}
236  virtual ~crack_singular_xy_function() {}
237  };
238 
239  struct cutoff_xy_function : public abstract_xy_function {
240  enum { NOCUTOFF = -1,
241  EXPONENTIAL_CUTOFF = 0,
242  POLYNOMIAL_CUTOFF = 1,
243  POLYNOMIAL2_CUTOFF= 2 };
244  int fun;
245  scalar_type a4, r1, r0;
246  virtual scalar_type val(scalar_type x, scalar_type y) const;
247  virtual base_small_vector grad(scalar_type x, scalar_type y) const;
248  virtual base_matrix hess(scalar_type x, scalar_type y) const;
249  cutoff_xy_function(int fun_num, scalar_type r,
250  scalar_type r1, scalar_type r0);
251  virtual ~cutoff_xy_function() {}
252  };
253 
254  struct interpolated_xy_function : public abstract_xy_function {
255  pinterpolator_on_mesh_fem itp;
256  size_type component;
257  virtual scalar_type val(scalar_type x, scalar_type y) const {
258  base_vector v; base_matrix g;
259  itp->eval(base_node(x,y), v, g);
260  return v[component];
261  }
262  virtual base_small_vector grad(scalar_type x, scalar_type y) const {
263  base_vector v; base_matrix g;
264  itp->eval(base_node(x,y), v, g);
265  return base_small_vector(g(component,0), g(component,1));
266  }
267  virtual base_matrix hess(scalar_type, scalar_type) const
268  { GMM_ASSERT1(false, "Sorry, to be done ..."); }
269  interpolated_xy_function(const pinterpolator_on_mesh_fem &itp_,
270  size_type c) :
271  itp(itp_), component(c) {}
272  virtual ~interpolated_xy_function() {}
273  };
274 
275  struct product_of_xy_functions : public abstract_xy_function {
276  pxy_function fn1, fn2;
277  scalar_type val(scalar_type x, scalar_type y) const {
278  return fn1->val(x,y) * fn2->val(x,y);
279  }
280  base_small_vector grad(scalar_type x, scalar_type y) const {
281  return fn1->grad(x,y)*fn2->val(x,y) + fn1->val(x,y)*fn2->grad(x,y);
282  }
283  virtual base_matrix hess(scalar_type x, scalar_type y) const {
284  base_matrix h = fn1->hess(x,y);
285  gmm::scale(h, fn2->val(x,y));
286  gmm::add(gmm::scaled(fn2->hess(x,y), fn1->val(x,y)), h);
287  gmm::rank_two_update(h, fn1->grad(x,y), fn2->grad(x,y));
288  return h;
289  }
290  product_of_xy_functions(pxy_function &fn1_, pxy_function &fn2_)
291  : fn1(fn1_), fn2(fn2_) {}
292  virtual ~product_of_xy_functions() {}
293  };
294 
295  struct add_of_xy_functions : public abstract_xy_function {
296  pxy_function fn1, fn2;
297  scalar_type val(scalar_type x, scalar_type y) const {
298  return fn1->val(x,y) + fn2->val(x,y);
299  }
300  base_small_vector grad(scalar_type x, scalar_type y) const {
301  return fn1->grad(x,y) + fn2->grad(x,y);
302  }
303  virtual base_matrix hess(scalar_type x, scalar_type y) const {
304  base_matrix h = fn1->hess(x,y);
305  gmm::add(fn2->hess(x,y), h);
306  return h;
307  }
308  add_of_xy_functions(const pxy_function &fn1_, const pxy_function &fn2_)
309  : fn1(fn1_), fn2(fn2_) {}
310  virtual ~add_of_xy_functions() {}
311  };
312 
313 
314  /** some useful global functions */
315  class level_set;
316 
317  pglobal_function
318  global_function_on_level_set(const level_set &ls, const pxy_function &fn);
319 
320  pglobal_function
321  global_function_on_level_sets(const std::vector<level_set> &lsets,
322  const pxy_function &fn);
323 
324  pglobal_function
325  global_function_bspline(const scalar_type xmin, const scalar_type xmax,
326  const size_type order, const size_type xtype);
327 
328  pglobal_function
329  global_function_bspline(const scalar_type xmin, const scalar_type xmax,
330  const scalar_type ymin, const scalar_type ymax,
331  const size_type order,
332  const size_type xtype, const size_type ytype);
333 
334  pglobal_function
335  global_function_bspline(const scalar_type xmin, const scalar_type xmax,
336  const scalar_type ymin, const scalar_type ymax,
337  const scalar_type zmin, const scalar_type zmax,
338  const size_type order,
339  const size_type xtype, const size_type ytype,
340  const size_type ztype);
341 } /* end of namespace getfem. */
342 
343 #endif
bgeot_rtree.h
region-tree for window/point search on a set of rectangles.
bgeot::geotrans_inv_convex
does the inversion of the geometric transformation for a given convex
Definition: bgeot_geotrans_inv.h:64
bgeot::rtree
Balanced tree of n-dimensional rectangles.
Definition: bgeot_rtree.h:98
dal::static_stored_object
base class for static stored objects
Definition: dal_static_stored_objects.h:206
getfem::abstract_xy_function
below a list of simple functions of (x,y) used for building the crack singular functions
Definition: getfem_global_function.h:205
getfem::fem_interpolation_context
structure passed as the argument of fem interpolation functions.
Definition: getfem_fem.h:750
getfem::global_function
inherit from this class to define new global functions.
Definition: getfem_global_function.h:49
getfem::mesh_fem
Describe a finite element method linked to a mesh.
Definition: getfem_mesh_fem.h:152
getfem_generic_assembly.h
A language for generic assembly of pde boundary value problems.
getfem_mesh_fem.h
Define the getfem::mesh_fem class.
gmm::add
void add(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:1277
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
getfem
GEneric Tool for Finite Element Methods.
Definition: getfem_accumulated_distro.h:47
getfem::interpolator_on_mesh_fem
a general structure for interpolation of a function defined by a mesh_fem and a vector U at any point...
Definition: getfem_global_function.h:181