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view src/SbpOperators/operators/standard_diagonal.toml @ 1602:3e7438e2a033 feature/boundary_conditions
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| author | Vidar Stiernström <vidar.stiernstrom@gmail.com> |
|---|---|
| date | Sat, 01 Jun 2024 17:39:54 -0700 |
| parents | fad18896d20a |
| children | 1388149b54ad |
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[meta] authors = "Ken Mattson" description = "Standard operators for equidistant grids" type = "equidistant" cite = """ Ken Mattsson, Jan Nordström, Summation by parts operators for finite difference approximations of second derivatives, Journal of Computational Physics, Volume 199, Issue 2, 2004, Pages 503-540, ISSN 0021-9991, https://doi.org/10.1016/j.jcp.2004.03.001. """ [[stencil_set]] order = 2 H.inner = "1" H.closure = ["1/2"] e.closure = ["1"] d1.closure = {s = ["3/2", "-2", "1/2"], c = 1} D1.inner_stencil = ["-1/2", "0", "1/2"] D1.closure_stencils = [ {s = ["-1", "1"], c = 1}, ] D2.inner_stencil = ["1", "-2", "1"] D2.closure_stencils = [ {s = ["1", "-2", "1"], c = 1}, ] D2variable.inner_stencil = [["1/2", "1/2", "0"],[ "-1/2", "-1", "-1/2"],["0", "1/2", "1/2"]] D2variable.closure_stencils = [ {s = [["2", "-1", "0"],["-3", "1", "0"],["1","0","0"]], c = 1}, ] D2.positivity = {theta_M = "0.3636363636", theta_R = "1.000000538455350", m_b = "2"} [[stencil_set]] order = 4 H.inner = "1" H.closure = ["17/48", "59/48", "43/48", "49/48"] e.closure = ["1"] d1.closure = {s = ["11/6", "-3", "3/2", "-1/3"], c = 1} D1.inner_stencil = ["1/12","-2/3","0","2/3","-1/12"] D1.closure_stencils = [ {s = [ "-24/17", "59/34", "-4/17", "-3/34", "0", "0"], c = 1}, {s = [ "-1/2", "0", "1/2", "0", "0", "0"], c = 2}, {s = [ "4/43", "-59/86", "0", "59/86", "-4/43", "0"], c = 3}, {s = [ "3/98", "0", "-59/98", "0", "32/49", "-4/49"], c = 4}, ] D2.inner_stencil = ["-1/12","4/3","-5/2","4/3","-1/12"] D2.closure_stencils = [ {s = [ "2", "-5", "4", "-1", "0", "0"], c = 1}, {s = [ "1", "-2", "1", "0", "0", "0"], c = 2}, {s = [ "-4/43", "59/43", "-110/43", "59/43", "-4/43", "0"], c = 3}, {s = [ "-1/49", "0", "59/49", "-118/49", "64/49", "-4/49"], c = 4}, ] D2variable.inner_stencil = [ ["-1/8", "1/6", "-1/8", "0", "0" ], [ "1/6", "1/2", "1/2", "1/6", "0" ], ["-1/24", "-5/6", "-3/4", "-5/6", "-1/24"], [ "0", "1/6", "1/2", "1/2", "1/6" ], [ "0", "0", "-1/8", "1/6", "-1/8" ], ] D2variable.closure_stencils = [ {c = 1, s = [ [ "920/289", "-59/68", "-81031200387/366633756146", "-69462376031/733267512292", "0", "0", "0", "0" ], ["-1740/289", "0", "6025413881/7482321554", "1612249989/7482321554", "0", "0", "0", "0" ], [ "1128/289", "59/68", "-6251815797/8526366422", "-639954015/17052732844", "0", "0", "0", "0" ], [ "-308/289", "0", "1244724001/7482321554", "-752806667/7482321554", "0", "0", "0", "0" ], [ "0", "0", "-148737261/10783345769", "148737261/10783345769", "0", "0", "0", "0" ], [ "0", "0", "-3/833", "3/833", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0" ], ]}, {c = 2, s = [ [ "12/17", "0", "102125659/440136562", "27326271/440136562", "0", "0", "0", "0" ], [ "-59/68", "0", "-156920047993625/159775733917868", "-12001237118451/79887866958934", "0", "0", "0", "0" ], [ "2/17", "0", "1489556735319/1857857371138", "149729180391/1857857371138", "0", "0", "0", "0" ], [ "3/68", "0", "-13235456910147/159775733917868", "3093263736297/79887866958934", "0", "0", "0", "0" ], [ "0", "0", "67535018271/2349643145851", "-67535018271/2349643145851", "0", "0", "0", "0" ], [ "0", "0", "441/181507", "-441/181507", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0" ], ]}, {c = 3, s = [ [ "-96/731", "59/172", "-6251815797/21566691538", "-639954015/43133383076", "0", "0", "0", "0" ], [ "118/731", "0", "87883847383821/79887866958934", "8834021643069/79887866958934", "0", "0", "0", "0" ], [ "-16/731", "-59/172", "-1134866646907639536627/727679167377258785038", "-13777050223300597/23487032885926596", "-26254/557679", "0", "0", "0" ], [ "-6/731", "0", "14509020271326561681/14850595252597118062", "17220493277981/79887866958934", "1500708/7993399", "0", "0", "0" ], [ "0", "0", "-4841930283098652915/21402328452272317207", "31597236232005/115132514146699", "-26254/185893", "0", "0", "0" ], [ "0", "0", "-2318724711/1653303156799", "960119/1147305747", "13564/23980197", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0" ], ]}, {c = 4, s = [ [ "-36/833", "0", "1244724001/21566691538", "-752806667/21566691538", "0", "0", "0", "0" ], [ "177/3332", "0", "-780891957698673/7829010961975532", "3724542049827/79887866958934", "0", "0", "0", "0" ], [ "-6/833", "0", 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"375177/743572", "1/6", "0", "0" ], [ "0", "0", "-8386761355510099813/128413970713633903242", "-2224717261773437/2763180339520776", "-280535/371786", "-5/6", "-1/24", "0" ], [ "0", "0", "13091810925/13226425254392", "35039615/213452232", "1118749/2230716", "1/2", "1/6", "0" ], [ "0", "0", "0", "0", "-1/8", "1/6", "-1/8", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0" ], ]}, {c = 6, s = [ [ "0", "0", "-1/784", "1/784", "0", "0", "0", "0" ], [ "0", "0", "8673/2904112", "-8673/2904112", "0", "0", "0", "0" ], [ "0", "0", "-33235054191/26452850508784", "960119/1280713392", "3391/6692148", "0", "0", "0" ], [ "0", "0", "-752806667/539854092016", "-1063649/8712336", "368395/2230716", "-1/8", "0", "0" ], [ "0", "0", "13091810925/13226425254392", "35039615/213452232", "1118749/2230716", "1/2", "1/6", "0" ], [ "0", "0", "-660204843/13226425254392", "-3290636/80044587", "-5580181/6692148", "-3/4", "-5/6", "-1/24"], [ "0", "0", "0", "0", "1/6", "1/2", "1/2", "1/6" ], [ "0", "0", "0", "0", "0", "-1/8", "1/6", "-1/8" ], ]} ] D2.positivity = {theta_M = "0.2505765857", theta_R = "0.577587500088313", m_b = "4"} [[stencil_set]] order = 6 H.inner = "1" H.closure = ["13649/43200", "12013/8640", "2711/4320", "5359/4320", "7877/8640", "43801/43200"] e.closure = ["1"] d1.closure = ["-25/12", "4", "-3", "4/3", "-1/4"] D2.positivity = {theta_M = "0.1878687080", theta_R = "0.3697", m_b = "7"}