XIAN-FEM-2026June/三维matlab代码/2022-11 PML&&ABC/二维极坐标变换2.nb

204 lines
6.3 KiB
Mathematica

(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 12.1' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 6262, 195]
NotebookOptionsPosition[ 5642, 175]
NotebookOutlinePosition[ 6084, 193]
CellTagsIndexPosition[ 6041, 190]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"\[Epsilon]r", "=",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\[Epsilon]", ",", "0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "\[Epsilon]", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "\[Epsilon]"}], "}"}]}], "}"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[Epsilon]c", "=",
RowBox[{"\[Epsilon]", "*",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\[Rho]", ",", "0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"1", "/", "\[Rho]"}], ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "\[Rho]"}], "}"}]}], "}"}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"\[CapitalLambda]", "=",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", "0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "b", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "c"}], "}"}]}], "}"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{"\[Epsilon]c2", "=",
RowBox[{"Dot", "[",
RowBox[{"\[CapitalLambda]", ",", "\[Epsilon]c"}],
"]"}]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Acr", "=",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Cos", "[", "\[Theta]", "]"}], ",",
RowBox[{
RowBox[{"-", "\[Rho]"}], "*",
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"Sin", "[", "\[Theta]", "]"}], ",",
RowBox[{"\[Rho]", "*",
RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Acrt", "=",
RowBox[{"Transpose", "[", "Acr", "]"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"detAcr", "=", "\[Rho]"}], ";"}], "\[IndentingNewLine]",
RowBox[{"\[Epsilon]r2", "=",
RowBox[{
RowBox[{"Simplify", "[",
RowBox[{
RowBox[{"Dot", "[",
RowBox[{
RowBox[{"Dot", "[",
RowBox[{"Acr", ",", "\[Epsilon]c2"}], "]"}], ",", "Acrt"}], "]"}],
"/", "detAcr"}], "]"}], "//", "MatrixForm"}]}]}], "Input",
CellChangeTimes->{{3.8784402217024097`*^9, 3.8784402453104086`*^9}, {
3.878440326058539*^9, 3.8784403965948486`*^9}, {3.8784404366522737`*^9,
3.878440456332716*^9}},
CellLabel->
"In[128]:=",ExpressionUUID->"0a0210ff-e47b-4200-860b-f3e9b65237a9"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"a", " ", "\[Epsilon]", " ", "\[Rho]"}], ",", "0", ",", "0"}],
"}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
FractionBox[
RowBox[{"b", " ", "\[Epsilon]"}], "\[Rho]"], ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",",
RowBox[{"c", " ", "\[Epsilon]", " ", "\[Rho]"}]}], "}"}]}],
"}"}]], "Output",
CellChangeTimes->{
3.878440326964399*^9, {3.878440381710183*^9, 3.878440397927933*^9}, {
3.8784404393473454`*^9, 3.878440459466902*^9}},
CellLabel->
"Out[131]=",ExpressionUUID->"5ac92830-df96-47ca-a880-db5d619a6fcb"],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]", GridBox[{
{
RowBox[{"\[Epsilon]", " ",
RowBox[{"(",
RowBox[{
RowBox[{"a", " ",
SuperscriptBox[
RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}], "+",
RowBox[{"b", " ",
SuperscriptBox[
RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}]}], ")"}]}],
RowBox[{
RowBox[{"(",
RowBox[{"a", "-", "b"}], ")"}], " ", "\[Epsilon]", " ",
RowBox[{"Cos", "[", "\[Theta]", "]"}], " ",
RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "0"},
{
RowBox[{
RowBox[{"(",
RowBox[{"a", "-", "b"}], ")"}], " ", "\[Epsilon]", " ",
RowBox[{"Cos", "[", "\[Theta]", "]"}], " ",
RowBox[{"Sin", "[", "\[Theta]", "]"}]}],
RowBox[{"\[Epsilon]", " ",
RowBox[{"(",
RowBox[{
RowBox[{"b", " ",
SuperscriptBox[
RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}], "+",
RowBox[{"a", " ",
SuperscriptBox[
RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}]}], ")"}]}], "0"},
{"0", "0",
RowBox[{"c", " ", "\[Epsilon]"}]}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{
3.878440326964399*^9, {3.878440381710183*^9, 3.878440397927933*^9}, {
3.8784404393473454`*^9, 3.878440459472927*^9}},
CellLabel->
"Out[135]//MatrixForm=",ExpressionUUID->"4075618a-7e9c-4da4-977a-\
a74af24a7b16"]
}, Open ]]
},
WindowSize->{981, 843},
WindowMargins->{{48, Automatic}, {17, Automatic}},
Magnification:>1.4 Inherited,
FrontEndVersion->"12.1 for Microsoft Windows (64-bit) (2020\:5e743\:670814\
\:65e5)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"36305296-0541-428d-bfa1-68f21545d19a"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 2579, 76, 326, "Input",ExpressionUUID->"0a0210ff-e47b-4200-860b-f3e9b65237a9"],
Cell[3162, 100, 659, 19, 69, "Output",ExpressionUUID->"5ac92830-df96-47ca-a880-db5d619a6fcb"],
Cell[3824, 121, 1802, 51, 167, "Output",ExpressionUUID->"4075618a-7e9c-4da4-977a-a74af24a7b16"]
}, Open ]]
}
]
*)