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BF_N_H_RT2_3D.h
1 // ***********************************************************************
2 // Raviart-Thomas element of second order on hexahedra, 3D
3 // ***********************************************************************
4 
5 static double N_H_RT2_3D_CM[11664] = {
6 //using tschebyscheff points (see NF_N_H_RT2_3D.h)
7  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,-0.0625,-0,-0,-0,0,0,0,0,0,-0,0,0,0,0,-0,-0,0,0,0.0625,-0,0,0,-0,0,0,0,0,0,0,0,0,0,0.94921875,0,0,0,0,-0,-1.5820312,-0,-1.5820312,-0,-0,-0,-0,-0,0,-0,2.6367188,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
8  0,0,0,0,-0,0,0,0,0,0,0,-0,-0,0.0625,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0.0625,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0.94921875,-0,0,-0,-1.5820312,0,-0,-0,-1.5820312,-0,0,-0,0,-0,0,2.6367188,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
9  0,0,0,-0,0.0625,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,0,-0.0625,-0,0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0.94921875,-0,0,-0,-1.5820312,0,-0,-1.5820312,0,-0,0,0,-0,0,2.6367188,-0,0,-0,
10  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0.1875,0,-0,0,0,0,0,0,0,-0,0,0,0,0,0,0,-0,-0,-0.1875,0,0,-0,-0,0,0,0,0,0,0,0,0,0,-0,4.7460938,0,-0,-0,-0,0,-0,0,-7.9101562,-0,-7.9101562,0,-0,0,0,-0,13.183594,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
11  0,0,0,0,-0,0,0,0,0,-0,-0.03608439,0,-0,0,0,0,0.03608439,-0,0,0,0,0,0,0,0,0,0,-0,-0.03608439,-0,-0,0,0,0,0.03608439,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-0,1.265625,-0,-0,0,-0,-0,-0,0,0,0,0,-2.109375,0,0,-0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
12  0,-0,0,-0.03608439,-0,0.03608439,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.03608439,-0,-0,-0,0,-0,-0.03608439,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,1.265625,0,0,-0,-0,-0,-0,-0,-0,-0,-2.109375,0,-0,0,0,0,0,
13  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0.03608439,0,0,-0,-0,-0,-0.03608439,0,0,0,0,0,-0,0,0,0,0,0,-0,0,-0.03608439,0,0.03608439,-0,0,-0,0,0,0,0,0,0,0,0,0,0,0,1.265625,0,-0,-0,-0,-0,-0,-0,-0,-0,-0,-2.109375,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
14  0,0,0,0,-0,0,0,0,0,-0,-0,0,-0,-0.1875,0,0,-0,-0,0,0,0,0,0,0,0,0,0,-0,0,0,0,-0.1875,-0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,-0,4.7460938,0,-0,0,-0,-0,-0,-7.9101562,-0,0,0,-7.9101562,0,0,-0,13.183594,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
15  0,-0.03608439,-0,-0,0,0,0,0.03608439,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0.03608439,0,-0.03608439,-0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,-0,1.265625,-0,-0,0,-0,-0,-0,-2.109375,0,0,0,0,0,0,0,-0,
16  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,-0,0.03608439,-0,-0.03608439,0,-0,0,0,0,0,0,-0,0,0,0,0,0,-0.03608439,-0,-0,-0,0,0,0.03608439,-0,0,0,0,0,0,0,0,0,0,-0,0,0,1.265625,-0,0,0,-0,0,0,0,-0,-2.109375,-0,-0,0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
17  0,0,0,0,-0,0,0,0,0,0,-0,0,-0.03608439,-0,0.03608439,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0.03608439,-0,-0.03608439,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-0,-0,0,1.265625,0,-0,-0,-0,0,-0,-2.109375,-0,0,-0,0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
18  -0,-0,-0,0,-0.1875,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,0,-0.1875,-0,0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-0,-0,0,4.7460938,0,-0,0,0,0,-0,-7.9101562,0,-0,-7.9101562,-0,-0,0,13.183594,
19  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,0,-0,0.1875,0,0,0,-0,0,0,0,0,-0,0,0,0,0,0,0,-0,-0,-0.1875,0,-0,-0,0,0,0,0,0,0,0,0,0,0,-0.94921875,-0,-0,-0,-0,0,1.5820312,0,1.5820312,0,0,0,0,0,-0,0,-2.6367188,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
20  0,0,0,0,-0,0,0,0,0,-0,0.04166667,0,0,-0.08333333,-0,-0,0.04166667,-0,0,0,0,0,0,0,0,0,0,-0,-0.04166667,0,0,0.08333333,-0,-0,-0.04166667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-1.5820312,0,-0,0,4.7460938,-0,0,0,2.6367188,0,-0,0,-0,0,-0,-7.9101562,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
21  -0,-0,-0,0.04166667,-0.08333333,0.04166667,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0.04166667,0,-0,0.08333333,0,-0,-0.04166667,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-1.5820312,0,-0,0,4.7460938,-0,0,2.6367188,-0,0,-0,-0,0,-0,-7.9101562,0,-0,0,
22  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.10825318,-0,-0,0,0,0,-0.10825318,-0,0,0,0,0,-0,0,0,0,0,-0,0,-0,0.10825318,0,-0.10825318,0,-0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,6.328125,0,-0,0,-0,0,0,0,0,0,-0,-10.546875,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
23  0,0,0,0,-0,0,0,0,0,-0,0.10825318,0,0,0,-0,-0,-0.10825318,0,0,0,0,0,0,0,0,0,0,0,-0.10825318,-0,-0,-0,0,-0,0.10825318,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,-0,-0,-0,-0,6.328125,0,0,-0,0,0,0,0,-0,-0,0,-10.546875,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
24  0.02083333,-0,-0.02083333,-0,0,0,-0.02083333,-0,0.02083333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.02083333,-0,0.02083333,-0,0,-0,0.02083333,0,-0.02083333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,-0,0,-0,-0,1.6875,-0,-0,0,-0,0,0,0,0,0,-0,0,-0,
25  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0.10825318,0,-0.10825318,0,-0,-0,0,0,0,0,-0,0,0,0,0,-0,0.10825318,0,0,0,-0,-0,-0.10825318,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,0,0,6.328125,0,0,0,0,0,0,-0,0,-10.546875,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
26  0,0,0,0,-0,0,0,0,0,0.02083333,0,-0.02083333,0,0,-0,-0.02083333,-0,0.02083333,0,0,0,0,0,0,0,0,0,0.02083333,0,-0.02083333,0,0,-0,-0.02083333,0,0.02083333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,-0,-0,0,-0,0,1.6875,0,-0,0,-0,0,0,-0,-0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
27  -0,0,-0,0.10825318,-0,-0.10825318,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.10825318,0,-0,0,0,0,-0.10825318,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-0,-0,-0,-0,0,0,6.328125,0,-0,0,-0,0,0,0,-0,0,-10.546875,0,
28  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0.04166667,0,-0,0.08333333,0,0,-0.04166667,-0,0,0,0,0,-0,0,0,0,0,0,0,-0,0.04166667,-0.08333333,0.04166667,-0,-0,0,0,0,0,0,0,0,0,0,0,-1.5820312,-0,-0,-0,-0,0,4.7460938,0,2.6367188,0,0,0,0,0,-0,0,-7.9101562,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
29  0,0,0,0,-0,0,0,0,0,-0,-0,0,0,-0.1875,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,-0,-0,-0,0,0.1875,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-0.94921875,0,-0,0,1.5820312,-0,0,0,1.5820312,0,-0,0,-0,0,-0,-2.6367188,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
30  -0,0.04166667,-0,0,-0.08333333,0,0,0.04166667,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,-0.04166667,0.08333333,-0.04166667,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-1.5820312,0,-0,0,2.6367188,-0,0,4.7460938,-0,0,-0,0,0,-0,-7.9101562,0,-0,0,
31  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.02083333,-0,0.02083333,-0,0,-0,0.02083333,-0,-0.02083333,0,0,0,0,-0,0,0,0,0,0.02083333,0,-0.02083333,0,-0,0,-0.02083333,0,0.02083333,0,0,0,0,0,0,0,0,0,-0,-0,-0,0,0,0,0,1.6875,0,0,0,0,-0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
32  0,0,0,0,-0,0,0,0,0,-0,0,-0,0.10825318,-0,-0.10825318,0,0,-0,0,0,0,0,0,0,0,0,0,-0,-0,0,0.10825318,0,-0.10825318,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-0,-0,-0,0,0,0,0,6.328125,0,0,-0,-0,0,0,-10.546875,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
33  -0,0.10825318,-0,0,-0,0,-0,-0.10825318,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0.10825318,0,-0.10825318,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-0,-0,-0,0,0,0,0,0,6.328125,0,-0,0,0,-0,-0,-10.546875,-0,0,
34  0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,0,-0.04166667,0.08333333,-0.04166667,0,0,-0,0,0,0,0,-0,0,0,0,0,0,0.04166667,-0,-0,-0.08333333,0,-0,0.04166667,0,0,0,0,0,0,0,0,0,0,-1.5820312,-0,-0,-0,-0,0,2.6367188,0,4.7460938,0,0,0,0,0,-0,0,-7.9101562,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
35  0,0,0,0,-0,0,0,0,0,-0,0,0,0.04166667,-0.08333333,0.04166667,-0,0,-0,0,0,0,0,0,0,0,0,0,-0,0,0,-0.04166667,0.08333333,-0.04166667,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-1.5820312,0,-0,0,2.6367188,0,0,0,4.7460938,0,-0,0,-0,0,-0,-7.9101562,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,
36  -0,-0,-0,0,-0.1875,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,-0,0.1875,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,-0,-0.94921875,0,-0,0,1.5820312,-0,0,1.5820312,-0,0,-0,-0,0,-0,-2.6367188,0,-0,0,
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97  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.07216878,0.14433757,-0.07216878,0,-0,-0,0.07216878,-0.14433757,0.07216878,0,0,0,0,0,0,0,0,0,0.07216878,-0,-0.07216878,-0.14433757,0,0.14433757,0.07216878,0,-0.07216878,0,0,0,0,0,0,0,0,0,0,0,2.109375,0,-0,-0,-0,-0,-0,-0,0,-0,-0,-6.328125,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
98  0,0,0,0,0,0,0,0,0,-0.08333333,0.16666667,-0.08333333,0.16666667,-0.33333333,0.16666667,-0.08333333,0.16666667,-0.08333333,0,0,0,0,0,0,0,0,0,-0.08333333,0.16666667,-0.08333333,0.16666667,-0.33333333,0.16666667,-0.08333333,0.16666667,-0.08333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,13.183594,0,-0,0,-0,-0,-0,-39.550781,0,-0,0,-39.550781,0,0,-0,118.65234,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
99  0.07216878,-0.14433757,0.07216878,-0,0,0,-0.07216878,0.14433757,-0.07216878,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,-0.07216878,-0,0.07216878,0.14433757,0,-0.14433757,-0.07216878,0,0.07216878,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,-0,2.109375,-0,-0,0,-0,-0,-0,-6.328125,0,0,0,0,0,0,0,-0,
100  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.08333333,0.16666667,-0.08333333,0.16666667,-0.33333333,0.16666667,-0.08333333,0.16666667,-0.08333333,0,0,0,0,0,0,0,0,0,-0.08333333,0.16666667,-0.08333333,0.16666667,-0.33333333,0.16666667,-0.08333333,0.16666667,-0.08333333,0,0,0,0,0,0,0,0,0,-0,13.183594,0,-0,-0,-0,0,-0,0,-39.550781,-0,-39.550781,0,-0,0,0,-0,118.65234,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,
101  0,0,0,0,0,0,0,0,0,0.07216878,-0.14433757,0.07216878,-0,0,0,-0.07216878,0.14433757,-0.07216878,0,0,0,0,0,0,0,0,0,0.07216878,-0.14433757,0.07216878,-0,0,0,-0.07216878,0.14433757,-0.07216878,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,-0,2.109375,-0,-0,0,-0,-0,-0,0,0,0,0,-6.328125,0,0,-0,0,-0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,
102  0.07216878,-0,-0.07216878,-0.14433757,0,0.14433757,0.07216878,0,-0.07216878,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.07216878,0.14433757,-0.07216878,-0,0,0,0.07216878,-0.14433757,0.07216878,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,2.109375,0,0,-0,-0,-0,-0,-0,-0,-0,-6.328125,0,-0,0,0,0,0,
103  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.12028131,0,0.12028131,0.24056261,0,-0.24056261,-0.12028131,-0,0.12028131,0,0,0,0,0,0,0,0,0,-0.12028131,0.24056261,-0.12028131,0,0,-0,0.12028131,-0.24056261,0.12028131,0,0,0,0,0,0,0,0,0,-0,-0,-0,0,0,10.546875,0,0,0,0,0,0,-0,0,-31.640625,-0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,0,
104  0,0,0,0,0,0,0,0,0,-0.12028131,0,0.12028131,0.24056261,-0,-0.24056261,-0.12028131,0,0.12028131,0,0,0,0,0,0,0,0,0,-0.12028131,-0,0.12028131,0.24056261,0,-0.24056261,-0.12028131,-0,0.12028131,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,-0,-0,-0,0,0,0,0,10.546875,0,-0,-0,-0,0,-0,-31.640625,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,0,
105  -0.12028131,0.24056261,-0.12028131,0,-0,0,0.12028131,-0.24056261,0.12028131,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.12028131,-0,0.12028131,0.24056261,0,-0.24056261,-0.12028131,-0,0.12028131,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,-0,-0,-0,0,0,0,0,0,10.546875,0,-0,0,0,-0,-0,-31.640625,-0,0,
106  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.12028131,0.24056261,-0.12028131,-0,0,0,0.12028131,-0.24056261,0.12028131,0,0,0,0,0,0,0,0,0,-0.12028131,0,0.12028131,0.24056261,0,-0.24056261,-0.12028131,-0,0.12028131,0,0,0,0,0,0,0,0,0,0,-0,-0,-0,10.546875,0,-0,0,-0,0,0,0,0,0,-0,-31.640625,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,
107  0,0,0,0,0,0,0,0,0,-0.12028131,0.24056261,-0.12028131,0,0,-0,0.12028131,-0.24056261,0.12028131,0,0,0,0,0,0,0,0,0,0.12028131,-0.24056261,0.12028131,-0,-0,0,-0.12028131,0.24056261,-0.12028131,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,-0,-0,-0,-0,10.546875,0,0,-0,-0,0,0,0,-0,-0,0,-31.640625,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,
108  -0.12028131,0,0.12028131,0.24056261,-0,-0.24056261,-0.12028131,-0,0.12028131,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.12028131,0.24056261,-0.12028131,-0,0,0,0.12028131,-0.24056261,0.12028131,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,-0,-0,-0,-0,0,0,0,10.546875,0,-0,0,-0,0,0,0,-0,0,-31.640625,0,
109  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.08333333,-0.16666667,0.08333333,-0.16666667,0.33333333,-0.16666667,0.08333333,-0.16666667,0.08333333,0,0,0,0,0,0,0,0,0,-0.08333333,0.16666667,-0.08333333,0.16666667,-0.33333333,0.16666667,-0.08333333,0.16666667,-0.08333333,0,0,0,0,0,0,0,0,0,-2.6367188,-0,-0,-0,-0,0,7.9101562,0,7.9101562,0,0,0,0,0,-0,0,-23.730469,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,
110  0,0,0,0,0,0,0,0,0,-0.08333333,0.16666667,-0.08333333,0.16666667,-0.33333333,0.16666667,-0.08333333,0.16666667,-0.08333333,0,0,0,0,0,0,0,0,0,0.08333333,-0.16666667,0.08333333,-0.16666667,0.33333333,-0.16666667,0.08333333,-0.16666667,0.08333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-2.6367188,0,-0,0,7.9101562,-0,0,0,7.9101562,0,-0,0,-0,0,-0,-23.730469,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,
111  -0.08333333,0.16666667,-0.08333333,0.16666667,-0.33333333,0.16666667,-0.08333333,0.16666667,-0.08333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.08333333,-0.16666667,0.08333333,-0.16666667,0.33333333,-0.16666667,0.08333333,-0.16666667,0.08333333,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-2.6367188,0,-0,0,7.9101562,-0,0,7.9101562,-0,0,-0,0,0,-0,-23.730469,0,-0,0,
112  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.13888889,-0.27777778,0.13888889,-0.27777778,0.55555556,-0.27777778,0.13888889,-0.27777778,0.13888889,0,0,0,0,0,0,0,0,0,0.13888889,-0.27777778,0.13888889,-0.27777778,0.55555556,-0.27777778,0.13888889,-0.27777778,0.13888889,0,0,0,0,0,0,0,0,0,0,-13.183594,-0,0,0,0,-0,0,-0,39.550781,0,39.550781,-0,0,-0,-0,0,-118.65234,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,
113  0,0,0,0,0,0,0,0,0,0.13888889,-0.27777778,0.13888889,-0.27777778,0.55555556,-0.27777778,0.13888889,-0.27777778,0.13888889,0,0,0,0,0,0,0,0,0,0.13888889,-0.27777778,0.13888889,-0.27777778,0.55555556,-0.27777778,0.13888889,-0.27777778,0.13888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-0,-13.183594,-0,0,-0,0,0,0,39.550781,-0,0,-0,39.550781,-0,-0,0,-118.65234,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,
114  0.13888889,-0.27777778,0.13888889,-0.27777778,0.55555556,-0.27777778,0.13888889,-0.27777778,0.13888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.13888889,-0.27777778,0.13888889,-0.27777778,0.55555556,-0.27777778,0.13888889,-0.27777778,0.13888889,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0,-13.183594,-0,0,-0,-0,-0,0,39.550781,-0,0,39.550781,0,0,-0,-118.65234
115 };
116 
117 static void N_H_RT2_3D_Funct(double xi, double eta, double zeta,
118  double *values)
119 {
120  //space: Q_{3,2,2}xQ_{2,3,2}xQ_{2,2,3}
121  int nBF = 108; // number of basis functions
122  // monomials x-component, y-component and z-component
123  double mon_x[]={
124  //const + 1st degree polynomials
125  1,0,0,xi,0,0,eta,0,0,zeta,0,0,
126  //2nd degree polynomials
127  xi*xi,0,0,xi*eta,0,0,xi*zeta,0,0,eta*eta,0,0,eta*zeta,0,0,zeta*zeta,0,0,
128  //3rd degree polynomials
129  xi*xi*xi,0,0,xi*xi*eta,0,0,xi*xi*zeta,0,0,
130  xi*eta*eta,0,0,xi*eta*zeta,0,0,xi*zeta*zeta,0,0,
131  eta*eta*zeta,0,0,eta*zeta*zeta,0,0,
132  //4th degree polynomials
133  xi*xi*xi*eta,0,0,xi*xi*xi*zeta,0,0,
134  xi*xi*eta*eta,0,0,xi*xi*eta*zeta,0,0,xi*xi*zeta*zeta,0,0,
135  xi*eta*eta*zeta,0,0,xi*eta*zeta*zeta,0,0,
136  eta*eta*zeta*zeta,0,0,
137  //5th degree polynomials
138  xi*xi*xi*eta*eta,0,0,xi*xi*xi*eta*zeta,0,0,xi*xi*xi*zeta*zeta,0,0,
139  xi*xi*eta*eta*zeta,0,0,xi*xi*eta*zeta*zeta,0,0,
140  xi*eta*eta*zeta*zeta,0,0,
141  //6th degree polynomials
142  xi*xi*xi*eta*eta*zeta,0,0,xi*xi*xi*eta*zeta*zeta,0,0,
143  xi*xi*eta*eta*zeta*zeta,0,0,
144  //7t h degree polynomials
145  xi*xi*xi*eta*eta*zeta*zeta,0,0};
146  double mon_y[]={
147  //const + 1st degree polynomials
148  0,1,0,0,xi,0,0,eta,0,0,zeta,0,
149  //2nd degree polynomials
150  0,xi*xi,0,0,xi*eta,0,0,xi*zeta,0,0,eta*eta,0,0,eta*zeta,0,0,zeta*zeta,0,
151  //3rd degree polynomials
152  0,eta*eta*eta,0,0,xi*xi*eta,0,0,xi*xi*zeta,0,
153  0,xi*eta*eta,0,0,xi*eta*zeta,0,0,xi*zeta*zeta,0,
154  0,eta*eta*zeta,0,0,eta*zeta*zeta,0,
155  //4th degree polynomials
156  0,xi*eta*eta*eta,0,0,eta*eta*eta*zeta,0,
157  0,xi*xi*eta*eta,0,0,xi*xi*eta*zeta,0,0,xi*xi*zeta*zeta,0,
158  0,xi*eta*eta*zeta,0,0,xi*eta*zeta*zeta,0,
159  0,eta*eta*zeta*zeta,0,
160  //5th degree polynomials
161  0,xi*xi*eta*eta*eta,0,0,xi*eta*eta*eta*zeta,0,0,eta*eta*eta*zeta*zeta,0,
162  0,xi*xi*eta*eta*zeta,0,0,xi*xi*eta*zeta*zeta,0,
163  0,xi*eta*eta*zeta*zeta,0,
164  //6th degree polynomials
165  0,xi*xi*eta*eta*eta*zeta,0,0,xi*eta*eta*eta*zeta*zeta,0,
166  0,xi*xi*eta*eta*zeta*zeta,0,
167  //7t h degree polynomials
168  0,xi*xi*eta*eta*eta*zeta*zeta,0};
169  double mon_z[]={
170  //const + 1st degree polynomials
171  0,0,1,0,0,xi,0,0,eta,0,0,zeta,
172  //2nd degree polynomials
173  0,0,xi*xi,0,0,xi*eta,0,0,xi*zeta,0,0,eta*eta,0,0,eta*zeta,0,0,zeta*zeta,
174  //3rd degree polynomials
175  0,0,zeta*zeta*zeta,0,0,xi*xi*eta,0,0,xi*xi*zeta,
176  0,0,xi*eta*eta,0,0,xi*eta*zeta,0,0,xi*zeta*zeta,
177  0,0,eta*eta*zeta,0,0,eta*zeta*zeta,
178  //4th degree polynomials
179  0,0,xi*zeta*zeta*zeta,0,0,eta*zeta*zeta*zeta,
180  0,0,xi*xi*eta*eta,0,0,xi*xi*eta*zeta,0,0,xi*xi*zeta*zeta,
181  0,0,xi*eta*eta*zeta,0,0,xi*eta*zeta*zeta,
182  0,0,eta*eta*zeta*zeta,
183  //5th degree polynomials
184  0,0,xi*xi*zeta*zeta*zeta,0,0,xi*eta*zeta*zeta*zeta,0,0,eta*eta*zeta*zeta*zeta,
185  0,0,xi*xi*eta*eta*zeta,0,0,xi*xi*eta*zeta*zeta,
186  0,0,xi*eta*eta*zeta*zeta,
187  //6th degree polynomials
188  0,0,xi*xi*eta*zeta*zeta*zeta,0,0,xi*eta*eta*zeta*zeta*zeta,
189  0,0,xi*xi*eta*eta*zeta*zeta,
190  //7t h degree polynomials
191  0,0,xi*xi*eta*eta*zeta*zeta*zeta};
192 
193  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
194  for(int i=0; i<nBF; i++)
195  {
196  for(int j=0; j<nBF; j++)
197  {
198  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
199  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
200  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
201  }
202  }
203 }
204 
205 static void N_H_RT2_3D_DeriveXi(double xi, double eta, double zeta,
206  double *values)
207 {
208  int nBF = 108; // number of basis functions
209  // monomials x-component, y-component and z-component
210  double mon_x[]={
211  //const + 1st degree polynomials
212  0,0,0,1,0,0,0,0,0,0,0,0,
213  //2nd degree polynomials
214  2*xi,0,0,eta,0,0,zeta,0,0,0,0,0,0,0,0,0,0,0,
215  //3rd degree polynomials
216  3*xi*xi,0,0,2*xi*eta,0,0,2*xi*zeta,0,0,
217  eta*eta,0,0,eta*zeta,0,0,zeta*zeta,0,0,
218  0,0,0,0,0,0,
219  //4th degree polynomials
220  3*xi*xi*eta,0,0,3*xi*xi*zeta,0,0,
221  2*xi*eta*eta,0,0,2*xi*eta*zeta,0,0,2*xi*zeta*zeta,0,0,
222  eta*eta*zeta,0,0,eta*zeta*zeta,0,0,
223  0,0,0,
224  //5th degree polynomials
225  3*xi*xi*eta*eta,0,0,3*xi*xi*eta*zeta,0,0,3*xi*xi*zeta*zeta,0,0,
226  2*xi*eta*eta*zeta,0,0,2*xi*eta*zeta*zeta,0,0,
227  eta*eta*zeta*zeta,0,0,
228  //6th degree polynomials
229  3*xi*xi*eta*eta*zeta,0,0,3*xi*xi*eta*zeta*zeta,0,0,
230  2*xi*eta*eta*zeta*zeta,0,0,
231  //7t h degree polynomials
232  3*xi*xi*eta*eta*zeta*zeta,0,0};
233  double mon_y[]={
234  //const + 1st degree polynomials
235  0,0,0,0,1,0,0,0,0,0,0,0,
236  //2nd degree polynomials
237  0,2*xi,0,0,eta,0,0,zeta,0,0,0,0,0,0,0,0,0,0,
238  //3rd degree polynomials
239  0,0,0,0,2*xi*eta,0,0,2*xi*zeta,0,
240  0,eta*eta,0,0,eta*zeta,0,0,zeta*zeta,0,
241  0,0,0,0,0,0,
242  //4th degree polynomials
243  0,eta*eta*eta,0,0,0,0,
244  0,2*xi*eta*eta,0,0,2*xi*eta*zeta,0,0,2*xi*zeta*zeta,0,
245  0,eta*eta*zeta,0,0,eta*zeta*zeta,0,
246  0,0,0,
247  //5th degree polynomials
248  0,2*xi*eta*eta*eta,0,0,eta*eta*eta*zeta,0,0,0,0,
249  0,2*xi*eta*eta*zeta,0,0,2*xi*eta*zeta*zeta,0,
250  0,eta*eta*zeta*zeta,0,
251  //6th degree polynomials
252  0,2*xi*eta*eta*eta*zeta,0,0,eta*eta*eta*zeta*zeta,0,
253  0,2*xi*eta*eta*zeta*zeta,0,
254  //7t h degree polynomials
255  0,2*xi*eta*eta*eta*zeta*zeta,0};
256  double mon_z[]={
257  //const + 1st degree polynomials
258  0,0,0,0,0,1,0,0,0,0,0,0,
259  //2nd degree polynomials
260  0,0,2*xi,0,0,eta,0,0,zeta,0,0,0,0,0,0,0,0,0,
261  //3rd degree polynomials
262  0,0,0,0,0,2*xi*eta,0,0,2*xi*zeta,
263  0,0,eta*eta,0,0,eta*zeta,0,0,zeta*zeta,
264  0,0,0,0,0,0,
265  //4th degree polynomials
266  0,0,zeta*zeta*zeta,0,0,0,
267  0,0,2*xi*eta*eta,0,0,2*xi*eta*zeta,0,0,2*xi*zeta*zeta,
268  0,0,eta*eta*zeta,0,0,eta*zeta*zeta,
269  0,0,0,
270  //5th degree polynomials
271  0,0,2*xi*zeta*zeta*zeta,0,0,eta*zeta*zeta*zeta,0,0,0,
272  0,0,2*xi*eta*eta*zeta,0,0,2*xi*eta*zeta*zeta,
273  0,0,eta*eta*zeta*zeta,
274  //6th degree polynomials
275  0,0,2*xi*eta*zeta*zeta*zeta,0,0,eta*eta*zeta*zeta*zeta,
276  0,0,2*xi*eta*eta*zeta*zeta,
277  //7t h degree polynomials
278  0,0,2*xi*eta*eta*zeta*zeta*zeta};
279 
280  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
281  for(int i=0; i<nBF; i++)
282  {
283  for(int j=0; j<nBF; j++)
284  {
285  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
286  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
287  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
288  }
289  }
290 }
291 
292 static void N_H_RT2_3D_DeriveEta(double xi, double eta, double zeta,
293  double *values)
294 {
295  int nBF = 108; // number of basis functions
296  // monomials x-component, y-component and z-component
297  double mon_x[]={
298  //const + 1st degree polynomials
299  0,0,0,0,0,0,1,0,0,0,0,0,
300  //2nd degree polynomials
301  0,0,0,xi,0,0,0,0,0,2*eta,0,0,zeta,0,0,0,0,0,
302  //3rd degree polynomials
303  0,0,0,xi*xi,0,0,0,0,0,
304  xi*2*eta,0,0,xi*zeta,0,0,0,0,0,
305  2*eta*zeta,0,0,zeta*zeta,0,0,
306  //4th degree polynomials
307  xi*xi*xi,0,0,0,0,0,
308  xi*xi*2*eta,0,0,xi*xi*zeta,0,0,0,0,0,
309  xi*2*eta*zeta,0,0,xi*zeta*zeta,0,0,
310  2*eta*zeta*zeta,0,0,
311  //5th degree polynomials
312  xi*xi*xi*2*eta,0,0,xi*xi*xi*zeta,0,0,0,0,0,
313  xi*xi*2*eta*zeta,0,0,xi*xi*zeta*zeta,0,0,
314  xi*2*eta*zeta*zeta,0,0,
315  //6th degree polynomials
316  xi*xi*xi*2*eta*zeta,0,0,xi*xi*xi*zeta*zeta,0,0,
317  xi*xi*2*eta*zeta*zeta,0,0,
318  //7t h degree polynomials
319  xi*xi*xi*2*eta*zeta*zeta,0,0};
320  double mon_y[]={
321  //const + 1st degree polynomials
322  0,0,0,0,0,0,0,1,0,0,0,0,
323  //2nd degree polynomials
324  0,0,0,0,xi,0,0,0,0,0,2*eta,0,0,zeta,0,0,0,0,
325  //3rd degree polynomials
326  0,3*eta*eta,0,0,xi*xi,0,0,0,0,
327  0,xi*2*eta,0,0,xi*zeta,0,0,0,0,
328  0,2*eta*zeta,0,0,zeta*zeta,0,
329  //4th degree polynomials
330  0,xi*3*eta*eta,0,0,3*eta*eta*zeta,0,
331  0,xi*xi*2*eta,0,0,xi*xi*zeta,0,0,0,0,
332  0,xi*2*eta*zeta,0,0,xi*zeta*zeta,0,
333  0,2*eta*zeta*zeta,0,
334  //5th degree polynomials
335  0,xi*xi*3*eta*eta,0,0,xi*3*eta*eta*zeta,0,0,3*eta*eta*zeta*zeta,0,
336  0,xi*xi*2*eta*zeta,0,0,xi*xi*zeta*zeta,0,
337  0,xi*2*eta*zeta*zeta,0,
338  //6th degree polynomials
339  0,xi*xi*3*eta*eta*zeta,0,0,xi*3*eta*eta*zeta*zeta,0,
340  0,xi*xi*2*eta*zeta*zeta,0,
341  //7t h degree polynomials
342  0,xi*xi*3*eta*eta*zeta*zeta,0};
343  double mon_z[]={
344  //const + 1st degree polynomials
345  0,0,0,0,0,0,0,0,1,0,0,0,
346  //2nd degree polynomials
347  0,0,0,0,0,xi,0,0,0,0,0,2*eta,0,0,zeta,0,0,0,
348  //3rd degree polynomials
349  0,0,0,0,0,xi*xi,0,0,0,
350  0,0,xi*2*eta,0,0,xi*zeta,0,0,0,
351  0,0,2*eta*zeta,0,0,zeta*zeta,
352  //4th degree polynomials
353  0,0,0,0,0,zeta*zeta*zeta,
354  0,0,xi*xi*2*eta,0,0,xi*xi*zeta,0,0,0,
355  0,0,xi*2*eta*zeta,0,0,xi*zeta*zeta,
356  0,0,2*eta*zeta*zeta,
357  //5th degree polynomials
358  0,0,0,0,0,xi*zeta*zeta*zeta,0,0,2*eta*zeta*zeta*zeta,
359  0,0,xi*xi*2*eta*zeta,0,0,xi*xi*zeta*zeta,
360  0,0,xi*2*eta*zeta*zeta,
361  //6th degree polynomials
362  0,0,xi*xi*zeta*zeta*zeta,0,0,xi*2*eta*zeta*zeta*zeta,
363  0,0,xi*xi*2*eta*zeta*zeta,
364  //7t h degree polynomials
365  0,0,xi*xi*2*eta*zeta*zeta*zeta};
366 
367  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
368  for(int i=0; i<nBF; i++)
369  {
370  for(int j=0; j<nBF; j++)
371  {
372  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
373  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
374  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
375  }
376  }
377 }
378 
379 static void N_H_RT2_3D_DeriveZeta(double xi, double eta, double zeta,
380  double *values)
381 {
382  int nBF = 108; // number of basis functions
383  // monomials x-component, y-component and z-component
384  double mon_x[]={
385  //const + 1st degree polynomials
386  0,0,0,0,0,0,0,0,0,1,0,0,
387  //2nd degree polynomials
388  0,0,0,0,0,0,xi,0,0,0,0,0,eta,0,0,2*zeta,0,0,
389  //3rd degree polynomials
390  0,0,0,0,0,0,xi*xi,0,0,
391  0,0,0,xi*eta,0,0,xi*2*zeta,0,0,
392  eta*eta,0,0,eta*2*zeta,0,0,
393  //4th degree polynomials
394  0,0,0,xi*xi*xi,0,0,
395  0,0,0,xi*xi*eta,0,0,xi*xi*2*zeta,0,0,
396  xi*eta*eta,0,0,xi*eta*2*zeta,0,0,
397  eta*eta*2*zeta,0,0,
398  //5th degree polynomials
399  0,0,0,xi*xi*xi*eta,0,0,xi*xi*xi*2*zeta,0,0,
400  xi*xi*eta*eta,0,0,xi*xi*eta*2*zeta,0,0,
401  xi*eta*eta*2*zeta,0,0,
402  //6th degree polynomials
403  xi*xi*xi*eta*eta,0,0,xi*xi*xi*eta*2*zeta,0,0,
404  xi*xi*eta*eta*2*zeta,0,0,
405  //7t h degree polynomials
406  xi*xi*xi*eta*eta*2*zeta,0,0};
407  double mon_y[]={
408  //const + 1st degree polynomials
409  0,0,0,0,0,0,0,0,0,0,1,0,
410  //2nd degree polynomials
411  0,0,0,0,0,0,0,xi,0,0,0,0,0,eta,0,0,2*zeta,0,
412  //3rd degree polynomials
413  0,0,0,0,0,0,0,xi*xi,0,
414  0,0,0,0,xi*eta,0,0,xi*2*zeta,0,
415  0,eta*eta,0,0,eta*2*zeta,0,
416  //4th degree polynomials
417  0,0,0,0,eta*eta*eta,0,
418  0,0,0,0,xi*xi*eta,0,0,xi*xi*2*zeta,0,
419  0,xi*eta*eta,0,0,xi*eta*2*zeta,0,
420  0,eta*eta*2*zeta,0,
421  //5th degree polynomials
422  0,0,0,0,xi*eta*eta*eta,0,0,eta*eta*eta*2*zeta,0,
423  0,xi*xi*eta*eta,0,0,xi*xi*eta*2*zeta,0,
424  0,xi*eta*eta*2*zeta,0,
425  //6th degree polynomials
426  0,xi*xi*eta*eta*eta,0,0,xi*eta*eta*eta*2*zeta,0,
427  0,xi*xi*eta*eta*2*zeta,0,
428  //7t h degree polynomials
429  0,xi*xi*eta*eta*eta*2*zeta,0};
430  double mon_z[]={
431  //const + 1st degree polynomials
432  0,0,0,0,0,0,0,0,0,0,0,1,
433  //2nd degree polynomials
434  0,0,0,0,0,0,0,0,xi,0,0,0,0,0,eta,0,0,2*zeta,
435  //3rd degree polynomials
436  0,0,3*zeta*zeta,0,0,0,0,0,xi*xi,
437  0,0,0,0,0,xi*eta,0,0,xi*2*zeta,
438  0,0,eta*eta,0,0,eta*2*zeta,
439  //4th degree polynomials
440  0,0,xi*3*zeta*zeta,0,0,eta*3*zeta*zeta,
441  0,0,0,0,0,xi*xi*eta,0,0,xi*xi*2*zeta,
442  0,0,xi*eta*eta,0,0,xi*eta*2*zeta,
443  0,0,eta*eta*2*zeta,
444  //5th degree polynomials
445  0,0,xi*xi*3*zeta*zeta,0,0,xi*eta*3*zeta*zeta,0,0,eta*eta*3*zeta*zeta,
446  0,0,xi*xi*eta*eta,0,0,xi*xi*eta*2*zeta,
447  0,0,xi*eta*eta*2*zeta,
448  //6th degree polynomials
449  0,0,xi*xi*eta*3*zeta*zeta,0,0,xi*eta*eta*3*zeta*zeta,
450  0,0,xi*xi*eta*eta*2*zeta,
451  //7t h degree polynomials
452  0,0,xi*xi*eta*eta*3*zeta*zeta};
453 
454  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
455  for(int i=0; i<nBF; i++)
456  {
457  for(int j=0; j<nBF; j++)
458  {
459  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
460  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
461  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
462  }
463  }
464 }
465 
466 static void N_H_RT2_3D_DeriveXiXi(double xi, double eta, double zeta,
467  double *values)
468 {
469  int nBF = 108; // number of basis functions
470  // monomials x-component, y-component and z-component
471  double mon_x[]={
472  //const + 1st degree polynomials
473  0,0,0,0,0,0,0,0,0,0,0,0,
474  //2nd degree polynomials
475  2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
476  //3rd degree polynomials
477  3*2*xi,0,0,2*eta,0,0,2*zeta,0,0,
478  0,0,0,0,0,0,0,0,0,
479  0,0,0,0,0,0,
480  //4th degree polynomials
481  3*2*xi*eta,0,0,3*2*xi*zeta,0,0,
482  2*eta*eta,0,0,2*eta*zeta,0,0,2*zeta*zeta,0,0,
483  0,0,0,0,0,0,
484  0,0,0,
485  //5th degree polynomials
486  3*2*xi*eta*eta,0,0,3*2*xi*eta*zeta,0,0,3*2*xi*zeta*zeta,0,0,
487  2*eta*eta*zeta,0,0,2*eta*zeta*zeta,0,0,
488  0,0,0,
489  //6th degree polynomials
490  3*2*xi*eta*eta*zeta,0,0,3*2*xi*eta*zeta*zeta,0,0,
491  2*eta*eta*zeta*zeta,0,0,
492  //7t h degree polynomials
493  3*2*xi*eta*eta*zeta*zeta,0,0};
494  double mon_y[]={
495  //const + 1st degree polynomials
496  0,0,0,0,0,0,0,0,0,0,0,0,
497  //2nd degree polynomials
498  0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
499  //3rd degree polynomials
500  0,0,0,0,2*eta,0,0,2*zeta,0,
501  0,0,0,0,0,0,0,0,0,
502  0,0,0,0,0,0,
503  //4th degree polynomials
504  0,0,0,0,0,0,
505  0,2*eta*eta,0,0,2*eta*zeta,0,0,2*zeta*zeta,0,
506  0,0,0,0,0,0,
507  0,0,0,
508  //5th degree polynomials
509  0,2*eta*eta*eta,0,0,0,0,0,0,0,
510  0,2*eta*eta*zeta,0,0,2*eta*zeta*zeta,0,
511  0,0,0,
512  //6th degree polynomials
513  0,2*eta*eta*eta*zeta,0,0,0,0,
514  0,2*eta*eta*zeta*zeta,0,
515  //7t h degree polynomials
516  0,2*xi*eta*eta*eta*zeta*zeta,0};
517  double mon_z[]={
518  //const + 1st degree polynomials
519  0,0,0,0,0,0,0,0,0,0,0,0,
520  //2nd degree polynomials
521  0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
522  //3rd degree polynomials
523  0,0,0,0,0,2*eta,0,0,2*zeta,
524  0,0,0,0,0,0,0,0,0,
525  0,0,0,0,0,0,
526  //4th degree polynomials
527  0,0,0,0,0,0,
528  0,0,2*eta*eta,0,0,2*eta*zeta,0,0,2*zeta*zeta,
529  0,0,0,0,0,0,
530  0,0,0,
531  //5th degree polynomials
532  0,0,2*zeta*zeta*zeta,0,0,0,0,0,0,
533  0,0,2*eta*eta*zeta,0,0,2*eta*zeta*zeta,
534  0,0,0,
535  //6th degree polynomials
536  0,0,2*zeta*zeta*zeta,0,0,0,
537  0,0,2*eta*eta*zeta*zeta,
538  //7t h degree polynomials
539  0,0,2*eta*eta*zeta*zeta*zeta};
540 
541  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
542  for(int i=0; i<nBF; i++)
543  {
544  for(int j=0; j<nBF; j++)
545  {
546  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
547  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
548  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
549  }
550  }
551 }
552 
553 static void N_H_RT2_3D_DeriveXiEta(double xi, double eta, double zeta,
554  double *values)
555 {
556  int nBF = 108; // number of basis functions
557  // monomials x-component, y-component and z-component
558  double mon_x[]={
559  //const + 1st degree polynomials
560  0,0,0,0,0,0,0,0,0,0,0,0,
561  //2nd degree polynomials
562  0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
563  //3rd degree polynomials
564  0,0,0,2*xi,0,0,0,0,0,
565  2*eta,0,0,zeta,0,0,0,0,0,
566  0,0,0,0,0,0,
567  //4th degree polynomials
568  3*xi*xi,0,0,0,0,0,
569  2*xi*2*eta,0,0,2*xi*zeta,0,0,0,0,0,
570  2*eta*zeta,0,0,zeta*zeta,0,0,
571  0,0,0,
572  //5th degree polynomials
573  3*xi*xi*2*eta,0,0,3*xi*xi*zeta,0,0,0,0,0,
574  2*xi*2*eta*zeta,0,0,2*xi*zeta*zeta,0,0,
575  2*eta*zeta*zeta,0,0,
576  //6th degree polynomials
577  3*xi*xi*2*eta*zeta,0,0,3*xi*xi*zeta*zeta,0,0,
578  2*xi*2*eta*zeta*zeta,0,0,
579  //7t h degree polynomials
580  3*xi*xi*2*eta*zeta*zeta,0,0};
581  double mon_y[]={
582  //const + 1st degree polynomials
583  0,0,0,0,0,0,0,0,0,0,0,0,
584  //2nd degree polynomials
585  0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
586  //3rd degree polynomials
587  0,0,0,0,2*xi,0,0,0,0,
588  0,2*eta,0,0,zeta,0,0,0,0,
589  0,0,0,0,0,0,
590  //4th degree polynomials
591  0,3*eta*eta,0,0,0,0,
592  0,2*xi*2*eta,0,0,2*xi*zeta,0,0,0,0,
593  0,2*eta*zeta,0,0,zeta*zeta,0,
594  0,0,0,
595  //5th degree polynomials
596  0,2*xi*3*eta*eta,0,0,3*eta*eta*zeta,0,0,0,0,
597  0,2*xi*2*eta*zeta,0,0,2*xi*zeta*zeta,0,
598  0,2*eta*zeta*zeta,0,
599  //6th degree polynomials
600  0,2*xi*3*eta*eta*zeta,0,0,3*eta*eta*zeta*zeta,0,
601  0,2*xi*2*eta*zeta*zeta,0,
602  //7t h degree polynomials
603  0,2*xi*3*eta*eta*zeta*zeta,0};
604  double mon_z[]={
605  //const + 1st degree polynomials
606  0,0,0,0,0,0,0,0,0,0,0,0,
607  //2nd degree polynomials
608  0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
609  //3rd degree polynomials
610  0,0,0,0,0,2*xi,0,0,0,
611  0,0,2*eta,0,0,zeta,0,0,0,
612  0,0,0,0,0,0,
613  //4th degree polynomials
614  0,0,0,0,0,0,
615  0,0,2*xi*2*eta,0,0,2*xi*zeta,0,0,0,
616  0,0,2*eta*zeta,0,0,zeta*zeta,
617  0,0,0,
618  //5th degree polynomials
619  0,0,0,0,0,zeta*zeta*zeta,0,0,0,
620  0,0,2*xi*2*eta*zeta,0,0,2*xi*zeta*zeta,
621  0,0,2*eta*zeta*zeta,
622  //6th degree polynomials
623  0,0,2*xi*zeta*zeta*zeta,0,0,2*eta*zeta*zeta*zeta,
624  0,0,2*xi*2*eta*zeta*zeta,
625  //7t h degree polynomials
626  0,0,2*xi*2*eta*zeta*zeta*zeta};
627 
628  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
629  for(int i=0; i<nBF; i++)
630  {
631  for(int j=0; j<nBF; j++)
632  {
633  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
634  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
635  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
636  }
637  }
638 }
639 
640 static void N_H_RT2_3D_DeriveXiZeta(double xi, double eta, double zeta,
641  double *values)
642 {
643  int nBF = 108; // number of basis functions
644  // monomials x-component, y-component and z-component
645  double mon_x[]={
646  //const + 1st degree polynomials
647  0,0,0,0,0,0,0,0,0,0,0,0,
648  //2nd degree polynomials
649  0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
650  //3rd degree polynomials
651  0,0,0,0,0,0,2*xi,0,0,
652  0,0,0,eta,0,0,2*zeta,0,0,
653  0,0,0,0,0,0,
654  //4th degree polynomials
655  0,0,0,3*xi*xi,0,0,
656  0,0,0,2*xi*eta,0,0,2*xi*2*zeta,0,0,
657  eta*eta,0,0,eta*2*zeta,0,0,
658  0,0,0,
659  //5th degree polynomials
660  0,0,0,3*xi*xi*eta,0,0,3*xi*xi*2*zeta,0,0,
661  2*xi*eta*eta,0,0,2*xi*eta*2*zeta,0,0,
662  eta*eta*2*zeta,0,0,
663  //6th degree polynomials
664  3*xi*xi*eta*eta,0,0,3*xi*xi*eta*2*zeta,0,0,
665  2*xi*eta*eta*2*zeta,0,0,
666  //7t h degree polynomials
667  3*xi*xi*eta*eta*2*zeta,0,0};
668  double mon_y[]={
669  //const + 1st degree polynomials
670  0,0,0,0,0,0,0,0,0,0,0,0,
671  //2nd degree polynomials
672  0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
673  //3rd degree polynomials
674  0,0,0,0,0,0,0,2*xi,0,
675  0,0,0,0,eta,0,0,2*zeta,0,
676  0,0,0,0,0,0,
677  //4th degree polynomials
678  0,0,0,0,0,0,
679  0,0,0,0,2*xi*eta,0,0,2*xi*2*zeta,0,
680  0,eta*eta,0,0,eta*2*zeta,0,
681  0,0,0,
682  //5th degree polynomials
683  0,0,0,0,eta*eta*eta,0,0,0,0,
684  0,2*xi*eta*eta,0,0,2*xi*eta*2*zeta,0,
685  0,eta*eta*2*zeta,0,
686  //6th degree polynomials
687  0,2*xi*eta*eta*eta,0,0,eta*eta*eta*2*zeta,0,
688  0,2*xi*eta*eta*2*zeta,0,
689  //7t h degree polynomials
690  0,2*xi*eta*eta*eta*2*zeta,0};
691  double mon_z[]={
692  //const + 1st degree polynomials
693  0,0,0,0,0,0,0,0,0,0,0,0,
694  //2nd degree polynomials
695  0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
696  //3rd degree polynomials
697  0,0,0,0,0,0,0,0,2*xi,
698  0,0,0,0,0,eta,0,0,2*zeta,
699  0,0,0,0,0,0,
700  //4th degree polynomials
701  0,0,3*zeta*zeta,0,0,0,
702  0,0,0,0,0,xi*eta,0,0,xi*2*zeta,
703  0,0,eta*eta,0,0,eta*2*zeta,
704  0,0,0,
705  //5th degree polynomials
706  0,0,2*xi*3*zeta*zeta,0,0,eta*3*zeta*zeta,0,0,0,
707  0,0,2*xi*eta*eta,0,0,2*xi*eta*2*zeta,
708  0,0,eta*eta*2*zeta,
709  //6th degree polynomials
710  0,0,2*xi*eta*3*zeta*zeta,0,0,eta*eta*3*zeta*zeta,
711  0,0,2*xi*eta*eta*2*zeta,
712  //7t h degree polynomials
713  0,0,2*xi*eta*eta*3*zeta*zeta};
714 
715  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
716  for(int i=0; i<nBF; i++)
717  {
718  for(int j=0; j<nBF; j++)
719  {
720  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
721  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
722  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
723  }
724  }
725 }
726 
727 static void N_H_RT2_3D_DeriveEtaEta(double xi, double eta, double zeta,
728  double *values)
729 {
730  int nBF = 108; // number of basis functions
731  // monomials x-component, y-component and z-component
732  double mon_x[]={
733  //const + 1st degree polynomials
734  0,0,0,0,0,0,0,0,0,0,0,0,
735  //2nd degree polynomials
736  0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,
737  //3rd degree polynomials
738  0,0,0,0,0,0,0,0,0,
739  xi*2,0,0,0,0,0,0,0,0,
740  2*zeta,0,0,0,0,0,
741  //4th degree polynomials
742  0,0,0,0,0,0,
743  xi*xi*2,0,0,0,0,0,0,0,0,
744  xi*2*zeta,0,0,0,0,0,
745  2*zeta*zeta,0,0,
746  //5th degree polynomials
747  xi*xi*xi*2,0,0,0,0,0,0,0,0,
748  xi*xi*2*zeta,0,0,0,0,0,
749  xi*2*zeta*zeta,0,0,
750  //6th degree polynomials
751  xi*xi*xi*2*zeta,0,0,0,0,0,
752  xi*xi*2*zeta*zeta,0,0,
753  //7t h degree polynomials
754  xi*xi*xi*2*zeta*zeta,0,0};
755  double mon_y[]={
756  //const + 1st degree polynomials
757  0,0,0,0,0,0,0,0,0,0,0,0,
758  //2nd degree polynomials
759  0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,
760  //3rd degree polynomials
761  0,3*2*eta,0,0,0,0,0,0,0,
762  0,xi*20,0,0,0,0,0,0,0,
763  0,2*zeta,0,0,zeta*zeta,0,
764  //4th degree polynomials
765  0,xi*3*2*eta,0,0,3*2*eta*zeta,0,
766  0,xi*xi*2,0,0,0,0,0,0,0,
767  0,xi*2*zeta,0,0,0,0,
768  0,2*zeta*zeta,0,
769  //5th degree polynomials
770  0,xi*xi*3*2*eta,0,0,xi*3*2*eta*zeta,0,0,3*2*eta*zeta*zeta,0,
771  0,xi*xi*2*zeta,0,0,0,0,
772  0,xi*2*zeta*zeta,0,
773  //6th degree polynomials
774  0,xi*xi*3*2*eta*zeta,0,0,xi*3*2*eta*zeta*zeta,0,
775  0,xi*xi*2*zeta*zeta,0,
776  //7t h degree polynomials
777  0,xi*xi*3*2*eta*zeta*zeta,0};
778  double mon_z[]={
779  //const + 1st degree polynomials
780  0,0,0,0,0,0,0,0,0,0,0,0,
781  //2nd degree polynomials
782  0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,
783  //3rd degree polynomials
784  0,0,0,0,0,0,0,0,0,
785  0,0,xi*2,0,0,0,0,0,0,
786  0,0,2*zeta,0,0,0,
787  //4th degree polynomials
788  0,0,0,0,0,0,
789  0,0,xi*xi*2,0,0,0,0,0,0,
790  0,0,xi*2*zeta,0,0,0,
791  0,0,2*zeta*zeta,
792  //5th degree polynomials
793  0,0,0,0,0,0,0,0,2*zeta*zeta*zeta,
794  0,0,xi*xi*2*zeta,0,0,0,
795  0,0,xi*2*zeta*zeta,
796  //6th degree polynomials
797  0,0,0,0,0,xi*2*zeta*zeta*zeta,
798  0,0,xi*xi*2*zeta*zeta,
799  //7t h degree polynomials
800  0,0,xi*xi*2*zeta*zeta*zeta};
801 
802  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
803  for(int i=0; i<nBF; i++)
804  {
805  for(int j=0; j<nBF; j++)
806  {
807  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
808  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
809  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
810  }
811  }
812 }
813 
814 static void N_H_RT2_3D_DeriveEtaZeta(double xi, double eta, double zeta,
815  double *values)
816 {
817  int nBF = 108; // number of basis functions
818  // monomials x-component, y-component and z-component
819  double mon_x[]={
820  //const + 1st degree polynomials
821  0,0,0,0,0,0,0,0,0,0,0,0,
822  //2nd degree polynomials
823  0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
824  //3rd degree polynomials
825  0,0,0,0,0,0,0,0,0,
826  0,0,0,xi,0,0,0,0,0,
827  2*eta,0,0,2*zeta,0,0,
828  //4th degree polynomials
829  0,0,0,0,0,0,
830  0,0,0,xi*xi,0,0,0,0,0,
831  xi*2*eta,0,0,xi*2*zeta,0,0,
832  2*eta*2*zeta,0,0,
833  //5th degree polynomials
834  0,0,0,xi*xi*xi,0,0,0,0,0,
835  xi*xi*2*eta,0,0,xi*xi*2*zeta,0,0,
836  xi*2*eta*2*zeta,0,0,
837  //6th degree polynomials
838  xi*xi*xi*2*eta,0,0,xi*xi*xi*2*zeta,0,0,
839  xi*xi*2*eta*2*zeta,0,0,
840  //7t h degree polynomials
841  xi*xi*xi*2*eta*2*zeta,0,0};
842  double mon_y[]={
843  //const + 1st degree polynomials
844  0,0,0,0,0,0,0,0,0,0,0,0,
845  //2nd degree polynomials
846  0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
847  //3rd degree polynomials
848  0,0,0,0,0,0,0,0,0,
849  0,0,0,0,xi,0,0,0,0,
850  0,2*eta,0,0,2*zeta,0,
851  //4th degree polynomials
852  0,0,0,0,3*eta*eta,0,
853  0,0,0,0,xi*xi,0,0,0,0,
854  0,xi*2*eta,0,0,xi*2*zeta,0,
855  0,2*eta*2*zeta,0,
856  //5th degree polynomials
857  0,0,0,0,xi*3*eta*eta,0,0,3*eta*eta*2*zeta,0,
858  0,xi*xi*2*eta,0,0,xi*xi*2*zeta,0,
859  0,xi*2*eta*2*zeta,0,
860  //6th degree polynomials
861  0,xi*xi*3*eta*eta,0,0,xi*3*eta*eta*2*zeta,0,
862  0,xi*xi*2*eta*2*zeta,0,
863  //7t h degree polynomials
864  0,xi*xi*3*eta*eta*2*zeta,0};
865  double mon_z[]={
866  //const + 1st degree polynomials
867  0,0,0,0,0,0,0,0,0,0,0,0,
868  //2nd degree polynomials
869  0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
870  //3rd degree polynomials
871  0,0,0,0,0,0,0,0,0,
872  0,0,0,0,0,xi,0,0,0,
873  0,0,2*eta,0,0,2*zeta,
874  //4th degree polynomials
875  0,0,0,0,0,3*zeta*zeta,
876  0,0,0,0,0,xi*xi,0,0,0,
877  0,0,xi*2*eta,0,0,xi*2*zeta,
878  0,0,2*eta*2*zeta,
879  //5th degree polynomials
880  0,0,0,0,0,xi*3*zeta*zeta,0,0,2*eta*3*zeta*zeta,
881  0,0,xi*xi*2*eta,0,0,xi*xi*2*zeta,
882  0,0,xi*2*eta*2*zeta,
883  //6th degree polynomials
884  0,0,xi*xi*3*zeta*zeta,0,0,xi*2*eta*3*zeta*zeta,
885  0,0,xi*xi*2*eta*2*zeta,
886  //7t h degree polynomials
887  0,0,xi*xi*2*eta*3*zeta*zeta};
888 
889  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
890  for(int i=0; i<nBF; i++)
891  {
892  for(int j=0; j<nBF; j++)
893  {
894  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
895  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
896  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
897  }
898  }
899 }
900 
901 static void N_H_RT2_3D_DeriveZetaZeta(double xi, double eta, double zeta,
902  double *values)
903 {
904  int nBF = 108; // number of basis functions
905  // monomials x-component, y-component and z-component
906  double mon_x[]={
907  //const + 1st degree polynomials
908  0,0,0,0,0,0,0,0,0,0,0,0,
909  //2nd degree polynomials
910  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,
911  //3rd degree polynomials
912  0,0,0,0,0,0,0,0,0,
913  0,0,0,0,0,0,xi*2,0,0,
914  0,0,0,eta*2,0,0,
915  //4th degree polynomials
916  0,0,0,0,0,0,
917  0,0,0,0,0,0,xi*xi*2,0,0,
918  0,0,0,xi*eta*2,0,0,
919  eta*eta*2,0,0,
920  //5th degree polynomials
921  0,0,0,0,0,0,xi*xi*xi*2,0,0,
922  0,0,0,xi*xi*eta*2,0,0,
923  xi*eta*eta*2,0,0,
924  //6th degree polynomials
925  0,0,0,xi*xi*xi*eta*2,0,0,
926  xi*xi*eta*eta*2,0,0,
927  //7t h degree polynomials
928  xi*xi*xi*eta*eta*2,0,0};
929  double mon_y[]={
930  //const + 1st degree polynomials
931  0,0,0,0,0,0,0,0,0,0,0,0,
932  //2nd degree polynomials
933  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,
934  //3rd degree polynomials
935  0,0,0,0,0,0,0,0,0,
936  0,0,0,0,0,0,0,xi*2,0,
937  0,0,0,0,eta*2,0,
938  //4th degree polynomials
939  0,0,0,0,0,0,
940  0,0,0,0,0,0,0,xi*xi*2,0,
941  0,0,0,0,xi*eta*2,0,
942  0,eta*eta*2,0,
943  //5th degree polynomials
944  0,0,0,0,0,0,0,eta*eta*eta*2,0,
945  0,0,0,0,xi*xi*eta*2,0,
946  0,xi*eta*eta*2,0,
947  //6th degree polynomials
948  0,0,0,0,xi*eta*eta*eta*2,0,
949  0,xi*xi*eta*eta*2,0,
950  //7t h degree polynomials
951  0,xi*xi*eta*eta*eta*2,0};
952  double mon_z[]={
953  //const + 1st degree polynomials
954  0,0,0,0,0,0,0,0,0,0,0,0,
955  //2nd degree polynomials
956  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,
957  //3rd degree polynomials
958  0,0,3*2*zeta,0,0,0,0,0,0,
959  0,0,0,0,0,0,0,0,xi*2,
960  0,0,0,0,0,eta*2,
961  //4th degree polynomials
962  0,0,xi*3*2*zeta,0,0,eta*3*2*zeta,
963  0,0,0,0,0,0,0,0,xi*xi*2,
964  0,0,0,0,0,xi*eta*2,
965  0,0,eta*eta*2,
966  //5th degree polynomials
967  0,0,xi*xi*3*2*zeta,0,0,xi*eta*3*2*zeta,0,0,eta*eta*3*2*zeta,
968  0,0,0,0,0,xi*xi*eta*2,
969  0,0,xi*eta*eta*2,
970  //6th degree polynomials
971  0,0,xi*xi*eta*3*2*zeta,0,0,xi*eta*eta*3*2*zeta,
972  0,0,xi*xi*eta*eta*2,
973  //7t h degree polynomials
974  0,0,xi*xi*eta*eta*3*2*zeta};
975 
976  memset(values, 0.0, 3*nBF*SizeOfDouble); // 3 is the space dimension
977  for(int i=0; i<nBF; i++)
978  {
979  for(int j=0; j<nBF; j++)
980  {
981  values[i ] += N_H_RT2_3D_CM[i+j*nBF]*mon_x[j];
982  values[i+ nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_y[j];
983  values[i+2*nBF] += N_H_RT2_3D_CM[i+j*nBF]*mon_z[j];
984  }
985  }
986 }
987 
988 TBaseFunct3D *BF_N_H_RT2_3D_Obj =
989 new TBaseFunct3D(108, BF_N_H_RT2_3D, BFUnitHexahedron,
990  N_H_RT2_3D_Funct, N_H_RT2_3D_DeriveXi,
991  N_H_RT2_3D_DeriveEta, N_H_RT2_3D_DeriveZeta,
992  N_H_RT2_3D_DeriveXiXi, N_H_RT2_3D_DeriveXiEta,
993  N_H_RT2_3D_DeriveXiZeta, N_H_RT2_3D_DeriveEtaEta,
994  N_H_RT2_3D_DeriveEtaZeta, N_H_RT2_3D_DeriveZetaZeta,
995  7, 1, 0, NULL, 3);
TBaseFunct3D
Definition: BaseFunct3D.h:27
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