(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 72693, 2017] NotebookOptionsPosition[ 64958, 1795] NotebookOutlinePosition[ 65352, 1812] CellTagsIndexPosition[ 65309, 1809] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell["\<\ TrigGaussRuleInfo[{rule_,numer_},point_] := Module [ {zeta,p=rule,i=point,g1,g2,g3,g4,s1,w2,w3,eps=10.^(-24), jkl={{1,2,3},{2,1,3},{1,3,2},{3,1,2},{2,3,1},{3,2,1}}, info={{Null,Null,Null},0} }, If [ p == 1, info={{1/3,1/3,1/3},1}]; If [ p == 3, info={{1,1,1}/6,1/3}; info[[1,i]]=2/3]; If [ p == -3, info={{1,1,1}/2,1/3}; info[[1,i]]=0]; If [ p == 6, g1 = (8-Sqrt[10]+Sqrt[38-44*Sqrt[2/5]])/18; g2 = (8-Sqrt[10]-Sqrt[38-44*Sqrt[2/5]])/18; If [ i < 4, info={{g1,g1,g1}, (620+Sqrt[213125-53320*Sqrt[10]])/3720}; info[[1,i]]=1-2*g1]; If [ i > 3, info={{g2,g2,g2}, (620-Sqrt[213125-53320*Sqrt[10]])/3720}; info[[1,i-3]]=1-2*g2]]; If [ p == -6, If[i<4, info={{1,1,1}/6,3/10}; info[[1,i]]=2/3]; If[i>3, info={{1,1,1}/2,1/30}; info[[1,i-3]]=0]]; If [ p == 7, g1=(6-Sqrt[15])/21; g2=(6+Sqrt[15])/21; If[i<4, info={{g1,g1,g1},(155-Sqrt[15])/1200}; info[[1,i]] = 1-2*g1]; If[i>3&&i<7, info={{g2,g2,g2},(155+Sqrt[15])/1200}; info[[1,i-3]]=1-2*g2]; If[i==7, info={{1/3,1/3,1/3},9/40}]]; If [ p == 12, g1=0.063089014491502228340331602870819157; g2=0.249286745170910421291638553107019076; g3=0.053145049844816947353249671631398147; g4=0.310352451033784405416607733956552153; If [ !numer, {g1,g2,g3,g4}=Rationalize[{g1,g2,g3,g4},eps]]; w1=(30*g2^3*(4*g3^2+(1-2*g4)^2+4*g3*(-1+g4))+ g3^2*(1-15*g4)+(-1+g4)*g4-g3*(-1+g4)*(-1+15*g4)+ 2*g2*(1+60*g3*g4*(-1+g3+g4))-6*g2^2*(3+10*(-1+g4)*g4+ 10*g3^2*(1+3*g4)+10*g3*(-1+g4)*(1+3*g4)))/ (180*(g1-g2)*(-(g2*(-1+2*g2)*(-1+g3)*g3)+(-1+g3)*(g2-2*g2^2- 2*g3+3*g2*g3)*g4-(g2*(-1+2*g2-3*g3)+2*g3)*g4^2+ 2*g1^2*(g2*(-2+3*g2)+g3-g3^2+g4-g3*g4-g4^2)+ g1*(-4*g2^2+(-1+g3)*g3+(-1+g3)*(1+3*g3)*g4+(1+3*g3)* g4^2-2*g2*(-1+g3^2+g3*(-1+g4)+(-1+g4)*g4)))); w2=(-1+12*(2-3*g1)*g1*w1+4*g3^2*(-1+3*w1)+4*g3*(-1+g4)*(-1+3*w1)+ 4*(-1+g4)*g4*(-1+3*w1))/(12*(g2*(-2+3*g2)+g3-g3^2+g4-g3*g4-g4^2)); w3=(1-3*w1-3*w2)/6; If [ i<4, info={{g1,g1,g1},w1}; info[[1,i]] = 1-2*g1]; If [ i>3&&i<7, info={{g2,g2,g2},w2}; info[[1,i-3]]=1-2*g2]; If [ i>6, {j,k,l}=jkl[[i-6]]; info={{0,0,0},w3}; info[[1,j]]=g3; info[[1,k]]=g4;info[[1,l]]=1-g3-g4]]; If [ numer, Return[N[info,20]], Return[Simplify[info]]]; ]; \ \>", "Input", CellChangeTimes->{{3.417598776438467*^9, 3.4175987767022676`*^9}, { 3.4175988361251507`*^9, 3.417598837164668*^9}, 3.4175989118118134`*^9, 3.417599160233939*^9, {3.417599192984885*^9, 3.41759920467704*^9}, { 3.447764307626423*^9, 3.447764308097674*^9}, {3.4477647205520477`*^9, 3.4477647379795513`*^9}, {3.447764924522809*^9, 3.447765000805663*^9}, { 3.4477657112255173`*^9, 3.447765713763384*^9}, 3.447765764318479*^9, 3.4477658521080647`*^9, {3.4477661034993153`*^9, 3.447766103938959*^9}, { 3.447766191857283*^9, 3.447766193544735*^9}, 3.4477663360620527`*^9, { 3.449171646587631*^9, 3.449171647661566*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"Print", "[", "\"\< \>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", "\"\\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", "\"\< Mathematica version\>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", "\"\< \>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ "Print", "[", "\"\< Test the quadrature rules for a triangle, returned\>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ "Print", "[", "\"\< by {{a,b,c},w} = TrigGaussRuleInfo[{rule,numer},i]\>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", "\"\< \>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", "\"\< INPUT:\>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", "\"\< \>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ "Print", "[", "\"\< RULE is 1, 3, -3, 6, -6, 7, and 12, the order\>\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ "Print", "[", "\"\< of the rule. 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