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annotate src/SbpOperators/operators/standard_diagonal.toml @ 1983:730c9848ad0b feature/grids/geometry_functions

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Update docstring for check_transfiniteinterpolation
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 26 Feb 2025 22:50:52 +0100
parents 1388149b54ad
children
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1 [meta]
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2 authors = "Ken Mattson"
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3 description = "Standard operators for equidistant grids"
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4 type = "equidistant"
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5 cite = """
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6 Ken Mattsson, Jan Nordström,
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7 Summation by parts operators for finite difference approximations of second derivatives,
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8 Journal of Computational Physics,
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9 Volume 199, Issue 2,
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10 2004,
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11 Pages 503-540,
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12 ISSN 0021-9991,
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13 https://doi.org/10.1016/j.jcp.2004.03.001.
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14 """
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15
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16 [[stencil_set]]
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17
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18 order = 2
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19
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20 H.inner = "1"
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21 H.closure = ["1/2"]
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22
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23 e.closure = ["1"]
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24 d1.closure = {s = ["3/2", "-2", "1/2"], c = 1}
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26
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27 D1.inner_stencil = ["-1/2", "0", "1/2"]
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28 D1.closure_stencils = [
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29 {s = ["-1", "1"], c = 1},
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30 ]
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31
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32 D2.inner_stencil = ["1", "-2", "1"]
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33 D2.closure_stencils = [
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34 {s = ["1", "-2", "1"], c = 1},
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35 ]
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36
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37 D2.positivity = {theta_M = "0.3636363636", theta_R = "1.000000538455350", m_b = "2"}
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38
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39 D2variable.inner_stencil = [["1/2", "1/2", "0"],[ "-1/2", "-1", "-1/2"],["0", "1/2", "1/2"]]
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40 D2variable.closure_stencils = [
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41 {s = [["2", "-1", "0"],["-3", "1", "0"],["1","0","0"]], c = 1},
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42 ]
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43
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44
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45 [[stencil_set]]
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46
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47 order = 4
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48
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49 H.inner = "1"
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50 H.closure = ["17/48", "59/48", "43/48", "49/48"]
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51
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52 e.closure = ["1"]
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53 d1.closure = {s = ["11/6", "-3", "3/2", "-1/3"], c = 1}
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54
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55 D1.inner_stencil = ["1/12","-2/3","0","2/3","-1/12"]
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56 D1.closure_stencils = [
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57 {s = [ "-24/17", "59/34", "-4/17", "-3/34", "0", "0"], c = 1},
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58 {s = [ "-1/2", "0", "1/2", "0", "0", "0"], c = 2},
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59 {s = [ "4/43", "-59/86", "0", "59/86", "-4/43", "0"], c = 3},
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60 {s = [ "3/98", "0", "-59/98", "0", "32/49", "-4/49"], c = 4},
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61 ]
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62
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63 D2.inner_stencil = ["-1/12","4/3","-5/2","4/3","-1/12"]
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64 D2.closure_stencils = [
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65 {s = [ "2", "-5", "4", "-1", "0", "0"], c = 1},
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66 {s = [ "1", "-2", "1", "0", "0", "0"], c = 2},
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67 {s = [ "-4/43", "59/43", "-110/43", "59/43", "-4/43", "0"], c = 3},
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68 {s = [ "-1/49", "0", "59/49", "-118/49", "64/49", "-4/49"], c = 4},
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69 ]
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70
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71 D2.positivity = {theta_M = "0.2505765857", theta_R = "0.577587500088313", m_b = "4"}
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72
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73 D2variable.inner_stencil = [
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74 ["-1/8", "1/6", "-1/8", "0", "0" ],
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75 [ "1/6", "1/2", "1/2", "1/6", "0" ],
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76 ["-1/24", "-5/6", "-3/4", "-5/6", "-1/24"],
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77 [ "0", "1/6", "1/2", "1/2", "1/6" ],
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78 [ "0", "0", "-1/8", "1/6", "-1/8" ],
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79 ]
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80 D2variable.closure_stencils = [
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81 {c = 1, s = [
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82 [ "920/289", "-59/68", "-81031200387/366633756146", "-69462376031/733267512292", "0", "0", "0", "0" ],
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83 ["-1740/289", "0", "6025413881/7482321554", "1612249989/7482321554", "0", "0", "0", "0" ],
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84 [ "1128/289", "59/68", "-6251815797/8526366422", "-639954015/17052732844", "0", "0", "0", "0" ],
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85 [ "-308/289", "0", "1244724001/7482321554", "-752806667/7482321554", "0", "0", "0", "0" ],
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86 [ "0", "0", "-148737261/10783345769", "148737261/10783345769", "0", "0", "0", "0" ],
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87 [ "0", "0", "-3/833", "3/833", "0", "0", "0", "0" ],
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88 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
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89 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
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90 ]},
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91 {c = 2, s = [
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92 [ "12/17", "0", "102125659/440136562", "27326271/440136562", "0", "0", "0", "0" ],
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93 [ "-59/68", "0", "-156920047993625/159775733917868", "-12001237118451/79887866958934", "0", "0", "0", "0" ],
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94 [ "2/17", "0", "1489556735319/1857857371138", "149729180391/1857857371138", "0", "0", "0", "0" ],
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95 [ "3/68", "0", "-13235456910147/159775733917868", "3093263736297/79887866958934", "0", "0", "0", "0" ],
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96 [ "0", "0", "67535018271/2349643145851", "-67535018271/2349643145851", "0", "0", "0", "0" ],
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97 [ "0", "0", "441/181507", "-441/181507", "0", "0", "0", "0" ],
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98 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
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99 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
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100 ]},
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101 {c = 3, s = [
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102 [ "-96/731", "59/172", "-6251815797/21566691538", "-639954015/43133383076", "0", "0", "0", "0" ],
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103 [ "118/731", "0", "87883847383821/79887866958934", "8834021643069/79887866958934", "0", "0", "0", "0" ],
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104 [ "-16/731", "-59/172", "-1134866646907639536627/727679167377258785038", "-13777050223300597/23487032885926596", "-26254/557679", "0", "0", "0" ],
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105 [ "-6/731", "0", "14509020271326561681/14850595252597118062", "17220493277981/79887866958934", "1500708/7993399", "0", "0", "0" ],
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106 [ "0", "0", "-4841930283098652915/21402328452272317207", "31597236232005/115132514146699", "-26254/185893", "0", "0", "0" ],
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107 [ "0", "0", "-2318724711/1653303156799", "960119/1147305747", "13564/23980197", "0", "0", "0" ],
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108 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
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109 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
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110 ]},
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111 {c = 4, s = [
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112 [ "-36/833", "0", "1244724001/21566691538", "-752806667/21566691538", "0", "0", "0", "0" ],
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113 [ "177/3332", "0", "-780891957698673/7829010961975532", "3724542049827/79887866958934", "0", "0", "0", "0" ],
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114 [ "-6/833", "0", "14509020271326561681/16922771334354855466", "2460070468283/13005001597966", "1500708/9108757", "0", "0", "0" ],
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115 [ "-9/3332", "0", "-217407431400324796377/207908333536359652868", "-1950062198436997/3914505480987766", "-7476412/9108757", "-2/49", "0", "0" ],
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116 [ "0", "0", "4959271814984644613/21402328452272317207", "47996144728947/115132514146699", "4502124/9108757", "8/49", "0", "0" ],
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117 [ "0", "0", "-2258420001/1653303156799", "-1063649/8893843", "1473580/9108757", "-6/49", "0", "0" ],
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118 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
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119 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
886
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120 ]},
883
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121 {c = 5, s = [
886
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122 [ "0", "0", "-49579087/10149031312", "49579087/10149031312", "0", "0", "0", "0" ],
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123 [ "0", "0", "1328188692663/37594290333616", "-1328188692663/37594290333616", "0", "0", "0", "0" ],
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124 [ "0", "0", "-1613976761032884305/7963657098519931984", "10532412077335/42840005263888", "-564461/4461432", "0", "0", "0" ],
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125 [ "0", "0", "4959271814984644613/20965546238960637264", "15998714909649/37594290333616", "375177/743572", "1/6", "0", "0" ],
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126 [ "0", "0", "-8386761355510099813/128413970713633903242", "-2224717261773437/2763180339520776", "-280535/371786", "-5/6", "-1/24", "0" ],
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127 [ "0", "0", "13091810925/13226425254392", "35039615/213452232", "1118749/2230716", "1/2", "1/6", "0" ],
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128 [ "0", "0", "0", "0", "-1/8", "1/6", "-1/8", "0" ],
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129 [ "0", "0", "0", "0", "0", "0", "0", "0" ],
886
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130 ]},
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131 {c = 6, s = [
886
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132 [ "0", "0", "-1/784", "1/784", "0", "0", "0", "0" ],
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133 [ "0", "0", "8673/2904112", "-8673/2904112", "0", "0", "0", "0" ],
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134 [ "0", "0", "-33235054191/26452850508784", "960119/1280713392", "3391/6692148", "0", "0", "0" ],
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135 [ "0", "0", "-752806667/539854092016", "-1063649/8712336", "368395/2230716", "-1/8", "0", "0" ],
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136 [ "0", "0", "13091810925/13226425254392", "35039615/213452232", "1118749/2230716", "1/2", "1/6", "0" ],
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137 [ "0", "0", "-660204843/13226425254392", "-3290636/80044587", "-5580181/6692148", "-3/4", "-5/6", "-1/24"],
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138 [ "0", "0", "0", "0", "1/6", "1/2", "1/2", "1/6" ],
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139 [ "0", "0", "0", "0", "0", "-1/8", "1/6", "-1/8" ],
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140 ]}
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141 ]
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142
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143
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144 [[stencil_set]]
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145
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146 order = 6
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147
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148 H.inner = "1"
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149 H.closure = ["13649/43200", "12013/8640", "2711/4320", "5359/4320", "7877/8640", "43801/43200"]
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150
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151
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152
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153
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154
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155 e.closure = ["1"]
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156 d1.closure = ["-25/12", "4", "-3", "4/3", "-1/4"]
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157
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158 D2.positivity = {theta_M = "0.1878687080", theta_R = "0.3697", m_b = "7"}