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BF_N_T_BDM2_2D.h
1 // ***********************************************************************
2 // P2 Raviart-Thomas vector element, nonconforming , 2D
3 // History: 14.11.2011 implementation (Ulrich)
4 // ***********************************************************************
5 
6 // base function values
7 // vector function, orthonormal to edges,
8 // functions 1,2, and 3 are orthogonal to edge 1
9 // functions 4,5, and 6 are orthogonal to edge 2
10 // functions 7,8, and 9 are orthogonal to edge 3
11 // functions 10,11 and 12 correspond to inner degrees of freedom
12 
13 // coefficient matrix
14 
15 // NOTE: If you want to use other evaluation points for degress of freedom on
16 // the edges of a cell, you also have to change basis functions in
17 // NF_N_T_BDM2_2D.h
18 
19 /*
20 // using equidistant points on edges and point evaluation for inner dofs
21 static double N_T_BDM2_2D_CM[144] = {
22 0,0,-0,-0,0,-0,-1,3,-3,-0,0,0,
23 -3,3,-1,0,-0,0,0,-0,0,-0,-0,-0,
24 -0.047619048,-0.047619048,1.3809524,0.23809524,-1.7619048,1.0952381,2.8095238,-9.1904762,14.52381,9.1428571,2.2857143,-0.57142857,
25 10,-16,6,0,-0,0,0,-0,0,0,0,-0,
26 1.047619,-2.952381,1.6190476,2.7619048,-1.2380952,-0.095238095,-1.8095238,6.1904762,-11.52381,-9.1428571,-2.2857143,0.57142857,
27 -8,16,-8,-0,0,-0,-0,0,0,0,-0,0,
28 0,0,0,0,-0,0,6,-16,10,0,0,0,
29 5.7619048,-4.2380952,0.9047619,-0.80952381,3.1904762,-8.5238095,-3.952381,10.047619,-5.3809524,-2.2857143,-0.57142857,9.1428571,
30 0,0,0,0,0,0,-8,16,-8,0,0,0,
31 -2.7619048,1.2380952,0.095238095,1.8095238,-6.1904762,11.52381,6.952381,-13.047619,6.3809524,2.2857143,0.57142857,-9.1428571,
32 -0.76190476,3.2380952,-9.9047619,-4.1904762,11.809524,-6.4761905,-7.047619,20.952381,-19.619048,-9.7142857,-11.428571,2.8571429,
33 -8.952381,11.047619,3.6190476,0.76190476,-3.2380952,9.9047619,4.1904762,-11.809524,6.4761905,2.8571429,9.7142857,-11.428571
34 };
35 */
36 /*
37 // using equidistant points on edges and integral evaluation for inner dofs
38 static double N_T_BDM2_2D_CM[144] = {
39 0,0,0,0,0,0,-1,3,-3,0,0,-0,
40 -3,3,-1,-0,0,0,0,0,0,0,0,-0,
41 -1.5,4,-2.5,-3,1,-1,2.5,-6,9.5,18,6,90,
42 10,-16,6,-0,0,0,0,0,0,0,0,-0,
43 2.5,-7,5.5,6,-4,2,-1.5,3,-6.5,-18,-6,-90,
44 -8,16,-8,0,0,0,0,0,0,0,0,-0,
45 0,0,0,0,0,0,6,-16,10,0,0,-0,
46 9.5,-6,2.5,-1,1,-3,-2.5,4,-1.5,6,18,-90,
47 0,0,0,0,0,0,-8,16,-8,0,0,-0,
48 -6.5,3,-1.5,2,-4,6,5.5,-7,2.5,-6,-18,90,
49 1,-2,-1,-0,4,-0,-3,14,-13,-12,-12,-180,
50 -13,14,-3,0,4,0,-1,-2,1,-12,-12,180
51 };
52 */
53 /*
54 // using Gauss-Points on edges and poinit evaluation for inner dofs
55 static double N_T_BDM2_2D_CM[144] = {
56 0,0,0,0,0,0,-0.18783611,0.66666667,-1.4788306,0,0,0,
57 -1.4788306,0.66666667,-0.18783611,-0,0,0,0,-0,0,-0,-0,-0,
58 -0.18329167,0.73015873,0.73884722,0.0011361102,-0.98412698,0.55441945,-0.16965835,0.92063492,7.3918806,9.1428571,2.2857143,-0.57142857,
59 4.6243278,-6.6666667,2.0423389,0,0,0,0,-0,0,0,0,-0,
60 0.37112778,-1.3968254,0.73998333,1.4776944,0.31746032,-0.36658334,0.35749445,-1.5873016,-5.91305,-9.1428571,-2.2857143,0.57142857,
61 -3.3333333,6.6666667,-3.3333333,0,-0,-0,0,0,-0,0,0,0,
62 0,0,0,0,0,0,2.0423389,-6.6666667,4.6243278,0,0,0,
63 2.956525,-0.34920635,-0.17874723,0.54533056,-2.2539683,-4.4342195,-1.483375,4.6031746,-2.4055139,-2.2857143,-0.57142857,9.1428571,
64 0,0,0,0,0,0,-3.3333333,6.6666667,-3.3333333,0,0,-0,
65 -1.4776944,-0.31746032,0.36658334,-0.35749445,1.5873016,5.91305,2.9622056,-5.2698413,2.59335,2.2857143,0.57142857,-9.1428571,
66 0.72862223,-2.984127,-5.1730667,-1.4845111,5.5873016,-2.9599333,-1.4981444,5.3968254,-9.6129667,-9.7142857,-11.428571,2.8571429,
67 -5.1685222,7.9365079,2.9463,-0.72862223,2.984127,5.1730667,1.4845111,-5.5873016,2.9599333,2.8571429,9.7142857,-11.428571
68 };
69 */
70 /*
71 // using Gauss-Points on edges and integral evaluation for inner dofs
72 static double N_T_BDM2_2D_CM[144] = {
73 0,0,0,0,0,0,-0.18783611,0.66666667,-1.4788306,0,0,-0,
74 -1.4788306,0.66666667,-0.18783611,0,0,0,0,-0,0,-0,-0,-0,
75 -0.51058472,1.6666667,-1.1560819,-1.4788306,-1.3333333,-0.18783611,0.24075971,1,4.7592403,18,6,90,
76 4.6243278,-6.6666667,2.0423389,0,0,0,0,-0,0,-0,-0,0,
77 0.69842083,-2.3333333,2.6349125,2.9576611,0.66666667,0.37567222,-0.052923606,-1.6666667,-3.2804097,-18,-6,-90,
78 -3.3333333,6.6666667,-3.3333333,-0,-0,-0,0,-0,-0,0,0,-0,
79 0,0,0,0,0,0,2.0423389,-6.6666667,4.6243278,0,0,-0,
80 4.7592403,1,0.24075971,-0.18783611,-1.3333333,-1.4788306,-1.1560819,1.6666667,-0.51058472,6,18,-90,
81 0,0,0,0,0,0,-3.3333333,6.6666667,-3.3333333,0,0,-0,
82 -3.2804097,-1.6666667,-0.052923606,0.37567222,0.66666667,2.9576611,2.6349125,-2.3333333,0.69842083,-6,-18,90,
83 0.64549722,-2,-0.64549722,-0,4,-0,-0.10584721,4.6666667,-6.5608195,-12,-12,-180,
84 -6.5608195,4.6666667,-0.10584721,0,4,0,-0.64549722,-2,0.64549722,-12,-12,180
85 };
86 */
87 
88 // using Tschebyscheff-points on edges and point evaluation for inner dofs
89 static double N_T_BDM2_2D_CM[144] = {
90 0,-0,0,-0,-0,0,-0.089316398,0.33333333,-1.2440169,0,0,-0,
91 -1.2440169,0.33333333,-0.089316398,0,-0,-0,-0,0,-0,-0,-0,0,
92 -0.19017083,0.84126984,0.63461527,-0.025213607,-0.87301587,0.46965805,-0.49273412,2.3650794,6.2705119,9.1428571,2.2857143,-0.57142857,
93 3.8213672,-5.3333333,1.5119661,-0,0,0,0,-0,0,0,0,-0,
94 0.27948722,-1.1746032,0.60940166,1.2692305,0.53968254,-0.38034165,0.58205051,-2.6984127,-5.026495,-9.1428571,-2.2857143,0.57142857,
95 -2.6666667,5.3333333,-2.6666667,0,-0,-0,-0,0,-0,-0,-0,0,
96 -0,-0,-0,-0,0,-0,1.5119661,-5.3333333,3.8213672,-0,-0,0,
97 2.5132475,0.20634921,-0.29102526,0.67136691,-3.031746,-3.782478,-1.1431625,3.8253968,-1.9679486,-2.2857143,-0.57142857,9.1428571,
98 0,0,0,0,-0,0,-2.6666667,5.3333333,-2.6666667,0,0,-0,
99 -1.2692305,-0.53968254,0.38034165,-0.58205051,2.6984127,5.026495,2.3871794,-4.1587302,2.057265,2.2857143,0.57142857,-9.1428571,
100 0.86153774,-3.8730159,-4.4170933,-1.1179489,4.6984127,-2.4376067,-0.81538561,3.1746032,-8.0735033,-9.7142857,-11.428571,2.8571429,
101 -4.5179477,7.4920635,2.7401699,-0.86153774,3.8730159,4.4170933,1.1179489,-4.6984127,2.4376067,2.8571429,9.7142857,-11.428571
102 };
103 
104 /*
105 // using Tschebyscheff-points on edges and integral evaluation for inner dofs
106 static double N_T_BDM2_2D_CM[144] = {
107 0,-0,-0,-0,-0,-0,-0.089316398,0.33333333,-1.2440169,0,0,0,
108 -1.2440169,0.33333333,-0.089316398,-0,-0,0,0,0,-0,0,0,-0,
109 -0.37799153,1.3333333,-0.9553418,-1.2440169,-1.6666667,-0.089316398,-0.020725942,2,4.0207259,18,6,90,
110 3.8213672,-5.3333333,1.5119661,-0,0,-0,-0,-0,0,-0,-0,0,
111 0.46730793,-1.6666667,2.1993587,2.4880339,1.3333333,0.1786328,0.11004234,-2.3333333,-2.776709,-18,-6,-90,
112 -2.6666667,5.3333333,-2.6666667,-0,-0,-0,-0,0,-0,0,0,-0,
113 -0,-0,0,-0,0,0,1.5119661,-5.3333333,3.8213672,-0,-0,-0,
114 4.0207259,2,-0.020725942,-0.089316398,-1.6666667,-1.2440169,-0.9553418,1.3333333,-0.37799153,6,18,-90,
115 0,-0,-0,-0,-0,-0,-2.6666667,5.3333333,-2.6666667,0,0,0,
116 -2.776709,-2.3333333,0.11004234,0.1786328,1.3333333,2.4880339,2.1993587,-1.6666667,0.46730793,-6,-18,90,
117 0.57735027,-2,-0.57735027,-0,4,-0,0.22008468,3.3333333,-5.553418,-12,-12,-180,
118 -5.553418,3.3333333,0.22008468,0,4,0,-0.57735027,-2,0.57735027,-12,-12,180
119 };
120 */
121 static void N_T_BDM2_2D_Funct(double xi, double eta, double *values)
122 {
123  int nBF = 12; // number of basis functions
124  // monomials x-component and y-component
125  double mon_x[12]={1, 0, xi, 0, xi*xi, 0, eta, 0, eta*eta, 0, xi*eta, 0};
126  double mon_y[12]={0, 1, 0, xi, 0, xi*xi, 0, eta, 0, eta*eta, 0, xi*eta};
127 
128  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
129  for(int i=0; i<nBF; i++)
130  {
131  for(int j=0; j<nBF; j++)
132  {
133  values[i ] += N_T_BDM2_2D_CM[i+j*nBF]*mon_x[j];
134  values[i+nBF] += N_T_BDM2_2D_CM[i+j*nBF]*mon_y[j];
135  }
136  }
137 }
138 
139 // values of the derivatives in xi direction
140 static void N_T_BDM2_2D_DeriveXi(double xi, double eta, double *values)
141 {
142  int nBF = 12; // number of basis functions
143  // monomials x-component and y-component
144  double mon_x[12]={0, 0 , 1, 0, 2*xi, 0, 0, 0, 0, 0, eta, 0};
145  double mon_y[12]={0, 0, 0 , 1, 0, 2*xi, 0, 0, 0, 0, 0, eta};
146 
147  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
148  for(int i=0; i<nBF; i++)
149  {
150  for(int j=0; j<nBF; j++)
151  {
152  values[i ] += N_T_BDM2_2D_CM[i+j*nBF]*mon_x[j];
153  values[i+nBF] += N_T_BDM2_2D_CM[i+j*nBF]*mon_y[j];
154  }
155  }
156 }
157 
158 // values of the derivatives in eta direction
159 static void N_T_BDM2_2D_DeriveEta(double xi, double eta, double *values)
160 {
161  int nBF = 12; // number of basis functions
162  // monomials x-component and y-component
163  double mon_x[12]={0, 0, 0, 0, 0, 0, 1, 0, 2*eta, 0, xi, 0};
164  double mon_y[12]={0, 0, 0, 0, 0, 0, 0, 1, 0, 2*eta, 0, xi};
165 
166  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
167  for(int i=0; i<nBF; i++)
168  {
169  for(int j=0; j<nBF; j++)
170  {
171  values[i ] += N_T_BDM2_2D_CM[i+j*nBF]*mon_x[j];
172  values[i+nBF] += N_T_BDM2_2D_CM[i+j*nBF]*mon_y[j];
173  }
174  }
175 }
176 
177 // values of derivatives in xi-xi direction
178 static void N_T_BDM2_2D_DeriveXiXi(double xi, double eta, double *values)
179 {
180  int nBF = 12; // number of basis functions
181  // monomials x-component and y-component
182  double mon_x[12]={0, 0 , 0, 0, 2, 0, 0, 0, 0, 0, 0, 0};
183  double mon_y[12]={0, 0, 0 , 0, 0, 2, 0, 0, 0, 0, 0, 0};
184 
185  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
186  for(int i=0; i<nBF; i++)
187  {
188  for(int j=0; j<nBF; j++)
189  {
190  values[i ] += N_T_BDM2_2D_CM[i+j*nBF]*mon_x[j];
191  values[i+nBF] += N_T_BDM2_2D_CM[i+j*nBF]*mon_y[j];
192  }
193  }
194 }
195 
196 // values of derivatives in eta-eta direction
197 static void N_T_BDM2_2D_DeriveEtaEta(double xi, double eta, double *values)
198 {
199  int nBF = 12; // number of basis functions
200  // monomials x-component and y-component
201  double mon_x[12]={0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0};
202  double mon_y[12]={0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0};
203 
204  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
205  for(int i=0; i<nBF; i++)
206  {
207  for(int j=0; j<nBF; j++)
208  {
209  values[i ] += N_T_BDM2_2D_CM[i+j*nBF]*mon_x[j];
210  values[i+nBF] += N_T_BDM2_2D_CM[i+j*nBF]*mon_y[j];
211  }
212  }
213 }
214 
215 // values of derivatives in xi-eta direction
216 static void N_T_BDM2_2D_DeriveXiEta(double xi, double eta, double *values)
217 {
218  int nBF = 12; // number of basis functions
219  // monomials x-component and y-component
220  double mon_x[12]={0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0};
221  double mon_y[12]={0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1};
222 
223  memset(values, 0.0, 2*nBF*SizeOfDouble); // 2 is the space dimension
224  for(int i=0; i<nBF; i++)
225  {
226  for(int j=0; j<nBF; j++)
227  {
228  values[i ] += N_T_BDM2_2D_CM[i+j*nBF]*mon_x[j];
229  values[i+nBF] += N_T_BDM2_2D_CM[i+j*nBF]*mon_y[j];
230  }
231  }
232 }
233 
234 // ***********************************************************************
235 
236 TBaseFunct2D *BF_N_T_BDM2_2D_Obj = new TBaseFunct2D
237  (12, BF_N_T_BDM2_2D, BFUnitTriangle,
238  N_T_BDM2_2D_Funct, N_T_BDM2_2D_DeriveXi,
239  N_T_BDM2_2D_DeriveEta, N_T_BDM2_2D_DeriveXiXi,
240  N_T_BDM2_2D_DeriveXiEta, N_T_BDM2_2D_DeriveEtaEta, 2, 2,
241  0, NULL, 2);
TBaseFunct2D
Definition: BaseFunct2D.h:27
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