1 | |
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2 | ! |
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3 | ! This program may be freely redistributed under the |
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4 | ! condition that the copyright notices (including this |
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5 | ! entire header) are not removed, and no compensation |
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6 | ! is received through use of the software. Private, |
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7 | ! research, and institutional use is free. You may |
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8 | ! distribute modified versions of this code UNDER THE |
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9 | ! CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE |
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10 | ! TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE |
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11 | ! ORIGINAL AUTHOR, BOTH SOURCE AND OBJECT CODE ARE |
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12 | ! MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR |
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13 | ! NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution |
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14 | ! of this code as part of a commercial system is |
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15 | ! permissible ONLY BY DIRECT ARRANGEMENT WITH THE |
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16 | ! AUTHOR. (If you are not directly supplying this |
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17 | ! code to a customer, and you are instead telling them |
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18 | ! how they can obtain it for free, then you are not |
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19 | ! required to make any arrangement with me.) |
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20 | ! |
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21 | ! Disclaimer: Neither I nor: Columbia University, the |
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22 | ! National Aeronautics and Space Administration, nor |
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23 | ! the Massachusetts Institute of Technology warrant |
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24 | ! or certify this code in any way whatsoever. This |
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25 | ! code is provided "as-is" to be used at your own risk. |
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26 | ! |
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27 | ! |
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28 | |
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29 | ! |
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30 | ! BFUN1D.h90: poly. basis-functions for reconstruction. |
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31 | ! |
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32 | ! Darren Engwirda |
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33 | ! 07-Sep-2016 |
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34 | ! de2363 [at] columbia [dot] edu |
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35 | ! |
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36 | ! |
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37 | |
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38 | pure subroutine bfun1d(isel,ndof,sval,bfun) |
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39 | |
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40 | ! |
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41 | ! ISEL basis-function "order", -1 => integral-basis , |
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42 | ! +0 => function-basis, +1 => 1st deriv.-basis , |
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43 | ! +2 => 2nd deriv.-basis. |
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44 | ! NDOF no. degrees-of-freedom in basis. |
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45 | ! SVAL local coord. at which to evaluate basis-func., |
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46 | ! such that -1.0 <= SVAL <= +1.0 . |
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47 | ! BFUN basis-vector evaluated at SVAL . |
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48 | ! |
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49 | |
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50 | implicit none |
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51 | |
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52 | !------------------------------------------- arguments ! |
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53 | integer, intent( in) :: isel,ndof |
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54 | real*8 , intent( in) :: sval |
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55 | real*8 , intent(out) :: bfun(:) |
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56 | |
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57 | select case (isel) |
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58 | case (-1) |
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59 | !------------------------------------ -1th-order basis ! |
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60 | select case (ndof) |
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61 | case (+1) |
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62 | bfun(1) = sval**1 / 1.d0 |
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63 | |
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64 | case (+2) |
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65 | bfun(1) = sval**1 / 1.d0 |
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66 | bfun(2) = sval**2 / 2.d0 |
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67 | |
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68 | case (+3) |
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69 | bfun(1) = sval**1 / 1.d0 |
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70 | bfun(2) = sval**2 / 2.d0 |
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71 | bfun(3) = sval**3 / 3.d0 |
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72 | |
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73 | case (+4) |
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74 | bfun(1) = sval**1 / 1.d0 |
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75 | bfun(2) = sval**2 / 2.d0 |
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76 | bfun(3) = sval**3 / 3.d0 |
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77 | bfun(4) = sval**4 / 4.d0 |
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78 | |
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79 | case (+5) |
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80 | bfun(1) = sval**1 / 1.d0 |
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81 | bfun(2) = sval**2 / 2.d0 |
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82 | bfun(3) = sval**3 / 3.d0 |
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83 | bfun(4) = sval**4 / 4.d0 |
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84 | bfun(5) = sval**5 / 5.d0 |
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85 | |
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86 | case (+6) |
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87 | bfun(1) = sval**1 / 1.d0 |
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88 | bfun(2) = sval**2 / 2.d0 |
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89 | bfun(3) = sval**3 / 3.d0 |
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90 | bfun(4) = sval**4 / 4.d0 |
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91 | bfun(5) = sval**5 / 5.d0 |
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92 | bfun(6) = sval**6 / 6.d0 |
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93 | |
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94 | case (+7) |
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95 | bfun(1) = sval**1 / 1.d0 |
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96 | bfun(2) = sval**2 / 2.d0 |
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97 | bfun(3) = sval**3 / 3.d0 |
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98 | bfun(4) = sval**4 / 4.d0 |
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99 | bfun(5) = sval**5 / 5.d0 |
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100 | bfun(6) = sval**6 / 6.d0 |
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101 | bfun(7) = sval**7 / 7.d0 |
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102 | |
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103 | end select |
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104 | |
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105 | case (+0) |
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106 | !------------------------------------ +0th-order basis ! |
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107 | select case (ndof) |
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108 | case (+1) |
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109 | bfun(1) = 1.d0 |
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110 | |
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111 | case (+2) |
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112 | bfun(1) = 1.d0 |
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113 | bfun(2) = sval**1 * 1.d0 |
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114 | |
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115 | case (+3) |
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116 | bfun(1) = 1.d0 |
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117 | bfun(2) = sval**1 * 1.d0 |
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118 | bfun(3) = sval**2 * 1.d0 |
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119 | |
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120 | case (+4) |
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121 | bfun(1) = 1.d0 |
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122 | bfun(2) = sval**1 * 1.d0 |
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123 | bfun(3) = sval**2 * 1.d0 |
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124 | bfun(4) = sval**3 * 1.d0 |
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125 | |
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126 | case (+5) |
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127 | bfun(1) = 1.d0 |
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128 | bfun(2) = sval**1 * 1.d0 |
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129 | bfun(3) = sval**2 * 1.d0 |
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130 | bfun(4) = sval**3 * 1.d0 |
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131 | bfun(5) = sval**4 * 1.d0 |
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132 | |
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133 | case (+6) |
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134 | bfun(1) = 1.d0 |
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135 | bfun(2) = sval**1 * 1.d0 |
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136 | bfun(3) = sval**2 * 1.d0 |
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137 | bfun(4) = sval**3 * 1.d0 |
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138 | bfun(5) = sval**4 * 1.d0 |
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139 | bfun(6) = sval**5 * 1.d0 |
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140 | |
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141 | case (+7) |
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142 | bfun(1) = 1.d0 |
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143 | bfun(2) = sval**1 * 1.d0 |
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144 | bfun(3) = sval**2 * 1.d0 |
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145 | bfun(4) = sval**3 * 1.d0 |
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146 | bfun(5) = sval**4 * 1.d0 |
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147 | bfun(6) = sval**5 * 1.d0 |
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148 | bfun(7) = sval**6 * 1.d0 |
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149 | |
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150 | end select |
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151 | |
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152 | case (+1) |
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153 | !------------------------------------ +1st-order basis ! |
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154 | select case (ndof) |
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155 | case (+1) |
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156 | bfun(1) = 0.d0 |
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157 | |
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158 | case (+2) |
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159 | bfun(1) = 0.d0 |
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160 | bfun(2) = 1.d0 |
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161 | |
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162 | case (+3) |
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163 | bfun(1) = 0.d0 |
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164 | bfun(2) = 1.d0 |
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165 | bfun(3) = sval**1 * 2.d0 |
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166 | |
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167 | case (+4) |
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168 | bfun(1) = 0.d0 |
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169 | bfun(2) = 1.d0 |
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170 | bfun(3) = sval**1 * 2.d0 |
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171 | bfun(4) = sval**2 * 3.d0 |
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172 | |
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173 | case (+5) |
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174 | bfun(1) = 0.d0 |
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175 | bfun(2) = 1.d0 |
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176 | bfun(3) = sval**1 * 2.d0 |
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177 | bfun(4) = sval**2 * 3.d0 |
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178 | bfun(5) = sval**3 * 4.d0 |
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179 | |
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180 | case (+6) |
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181 | bfun(1) = 0.d0 |
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182 | bfun(2) = 1.d0 |
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183 | bfun(3) = sval**1 * 2.d0 |
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184 | bfun(4) = sval**2 * 3.d0 |
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185 | bfun(5) = sval**3 * 4.d0 |
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186 | bfun(6) = sval**4 * 5.d0 |
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187 | |
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188 | case (+7) |
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189 | bfun(1) = 0.d0 |
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190 | bfun(2) = 1.d0 |
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191 | bfun(3) = sval**1 * 2.d0 |
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192 | bfun(4) = sval**2 * 3.d0 |
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193 | bfun(5) = sval**3 * 4.d0 |
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194 | bfun(6) = sval**4 * 5.d0 |
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195 | bfun(7) = sval**5 * 6.d0 |
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196 | |
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197 | end select |
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198 | |
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199 | case (+2) |
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200 | !------------------------------------ +2nd-order basis ! |
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201 | select case (ndof) |
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202 | case (+1) |
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203 | bfun(1) = 0.d0 |
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204 | |
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205 | case (+2) |
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206 | bfun(1) = 0.d0 |
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207 | bfun(2) = 0.d0 |
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208 | |
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209 | case (+3) |
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210 | bfun(1) = 0.d0 |
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211 | bfun(2) = 0.d0 |
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212 | bfun(3) = 2.d0 |
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213 | |
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214 | case (+4) |
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215 | bfun(1) = 0.d0 |
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216 | bfun(2) = 0.d0 |
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217 | bfun(3) = 2.d0 |
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218 | bfun(4) = sval**1 * 6.d0 |
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219 | |
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220 | case (+5) |
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221 | bfun(1) = 0.d0 |
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222 | bfun(2) = 0.d0 |
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223 | bfun(3) = 2.d0 |
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224 | bfun(4) = sval**1 * 6.d0 |
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225 | bfun(5) = sval**2 *12.d0 |
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226 | |
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227 | case (+6) |
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228 | bfun(1) = 0.d0 |
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229 | bfun(2) = 0.d0 |
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230 | bfun(3) = 2.d0 |
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231 | bfun(4) = sval**1 * 6.d0 |
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232 | bfun(5) = sval**2 *12.d0 |
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233 | bfun(6) = sval**3 *20.d0 |
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234 | |
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235 | case (+7) |
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236 | bfun(1) = 0.d0 |
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237 | bfun(2) = 0.d0 |
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238 | bfun(3) = 2.d0 |
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239 | bfun(4) = sval**1 * 6.d0 |
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240 | bfun(5) = sval**2 *12.d0 |
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241 | bfun(6) = sval**3 *20.d0 |
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242 | bfun(7) = sval**4 *30.d0 |
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243 | |
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244 | end select |
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245 | |
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246 | end select |
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247 | |
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248 | end subroutine |
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249 | |
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250 | |
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251 | |
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