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Add more descriptive text to notebook with examples
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‎Examples.nb

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(* Content-type: application/vnd.wolfram.mathematica *)
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(*** Wolfram Notebook File ***)
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(* http://www.wolfram.com/nb *)
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(* CreatedBy='Mathematica 11.1' *)
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(*CacheID: 234*)
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(* Internal cache information:
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NotebookFileLineBreakTest
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NotebookFileLineBreakTest
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NotebookDataPosition[ 158, 7]
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NotebookDataLength[ 11138, 287]
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NotebookOptionsPosition[ 8744, 242]
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NotebookOutlinePosition[ 9086, 257]
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CellTagsIndexPosition[ 9043, 254]
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WindowFrame->Normal*)
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(* Beginning of Notebook Content *)
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Notebook[{
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Cell[CellGroupData[{
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Cell["Load package", "Subsection",ExpressionUUID->"9e86b217-f3c6-4773-a30b-530130954cb2"],
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Cell["Load GmshLink package", \
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"Subsection",ExpressionUUID->"9e86b217-f3c6-4773-a30b-530130954cb2"],
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Cell["Load pacakge from the same directory as this notebook.", \
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"Text",ExpressionUUID->"18b35fa7-ec7b-4cad-9d2e-6b60509b4a44"],
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Cell[BoxData[
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RowBox[{"Get", "[",
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RowBox[{"\"\<GmshLink.wl\>\"", ",",
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RowBox[{"Path", "\[Rule]",
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RowBox[{"NotebookDirectory", "[", "]"}]}]}], "]"}]], "Input",
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CellLabel->"In[69]:=",ExpressionUUID->"af1fa4ed-6365-4604-adc6-ecb5ad4dadc8"],
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CellLabel->"In[1]:=",ExpressionUUID->"af1fa4ed-6365-4604-adc6-ecb5ad4dadc8"],
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Cell["\<\
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Set your path to your directory containing Gmsh executable. Do not include \
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the name of executable itself.\
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\>", "Text",ExpressionUUID->"c78cb9f7-840d-4625-820c-e046b481604f"],
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Cell[BoxData[
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RowBox[{
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RowBox[{"(*", " ",
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RowBox[{
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"Set", " ", "your", " ", "path", " ", "to", " ", "Gmsh", " ", "executable",
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" ",
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RowBox[{"here", "."}]}], " ", "*)"}], "\[IndentingNewLine]",
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RowBox[{
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RowBox[{"$GmshDirectory", "=",
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RowBox[{"FileNameJoin", "[",
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RowBox[{"{",
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RowBox[{
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"$UserDocumentsDirectory", ",", "\"\<Software\>\"", ",", "\"\<GMSH\>\"",
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",", "\"\<gmsh-4.1.4-Windows64\>\""}], "}"}], "]"}]}],
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";"}]}]], "Input",
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CellLabel->"In[70]:=",ExpressionUUID->"55cc1a10-36cd-4a4c-9bcf-316cf2b3de4c"]
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RowBox[{"$GmshDirectory", "=",
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RowBox[{"FileNameJoin", "[",
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RowBox[{"{",
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RowBox[{
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"$UserDocumentsDirectory", ",", "\"\<Software\>\"", ",", "\"\<GMSH\>\"",
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",", "\"\<gmsh-4.4.1-Windows64\>\""}], "}"}], "]"}]}],
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";"}]], "Input",ExpressionUUID->"55cc1a10-36cd-4a4c-9bcf-316cf2b3de4c"],
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Cell["Check if \[OpenCurlyDoubleQuote]ImportMesh\[CloseCurlyDoubleQuote] \
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package is also installed.", \
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"Text",ExpressionUUID->"810750e7-656b-447d-b386-dd7209159fd7"],
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Cell[BoxData[
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RowBox[{"PacletInformation", "[", "\"\<ImportMesh\>\"", "]"}]], "Input",
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CellLabel->"In[21]:=",ExpressionUUID->"009c7b5a-46d0-44a1-b9c4-ae975cc4e965"]
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}, Open ]],
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Cell[CellGroupData[{
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Cell["Example", "Subsection",ExpressionUUID->"7a56a90d-0c47-4727-8fc2-650f30b3ab24"],
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Cell["Example", \
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"Subsection",ExpressionUUID->"7a56a90d-0c47-4727-8fc2-650f30b3ab24"],
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Cell[CellGroupData[{
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Cell["Region", "Subsubsection",ExpressionUUID->"8c33aff5-1ee8-4009-810f-29462c088165"],
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Cell["Define symbolic geometric Region", \
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"Subsubsection",ExpressionUUID->"8c33aff5-1ee8-4009-810f-29462c088165"],
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Cell["Define a symbolic region in 3D.", \
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"Text",ExpressionUUID->"3160b6f4-4820-47ed-bd3d-fbc0c80aaec4"],
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Cell[BoxData[
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@@ -94,16 +90,25 @@ Cell[BoxData[
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RowBox[{"{",
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CellLabel->"In[3]:=",ExpressionUUID->"873f4626-5b8b-4da8-8bdd-bb5969984ae4"],
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Cell["\<\
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Visualise region. This sometimes work poorly in case of more complicated \
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regions (version 12.0).\
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\>", "Text",ExpressionUUID->"40f7b4cd-4811-4ca5-86b5-209a45f5e78a"],
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Cell[BoxData[
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}, Open ]],
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Cell[CellGroupData[{
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Cell["Mathematica", "Subsubsection",ExpressionUUID->"0c830c6b-61b2-4f54-8754-19bc621d45f6"],
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Cell["Mathematica meshing method", \
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Cell["Create ElementMesh with build-in mesher. ", \
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"Text",ExpressionUUID->"7c7557c5-7b86-44ac-99a9-356d80af4a9e"],
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Cell[BoxData[
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RowBox[{"mesh", "=",
@@ -112,7 +117,10 @@ Cell[BoxData[
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RowBox[{"\"\<MeshOrder\>\"", "\[Rule]", "1"}], ",", "\[IndentingNewLine]",
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RowBox[{"MeshQualityGoal", "\[Rule]", "\"\<Maximal\>\""}]}],
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CellLabel->"In[73]:=",ExpressionUUID->"ce9f3e82-9335-42d3-bb9a-c470da973333"],
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CellLabel->"In[18]:=",ExpressionUUID->"ce9f3e82-9335-42d3-bb9a-c470da973333"],
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Cell["Minimal and average quality of elemens is not very good.", \
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"Text",ExpressionUUID->"4823fc17-e3ec-492e-9c8d-9585f91f5be0"],
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Cell[BoxData[{
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@@ -123,16 +131,27 @@ Cell[BoxData[{
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RowBox[{"Through", "[",
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RowBox[{
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RowBox[{"{",
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RowBox[{"Min", ",", "Mean"}], "}"}], "@", "quality"}], "]"}]}], "Input",
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CellLabel->"In[74]:=",ExpressionUUID->"8fd7c7cf-8541-4688-9eee-770ae51fa545"],
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RowBox[{"Min", ",", "Mean", ",", "Max"}], "}"}], "@", "quality"}],
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"]"}]}], "Input",
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CellLabel->"In[19]:=",ExpressionUUID->"8fd7c7cf-8541-4688-9eee-770ae51fa545"],
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Cell["\<\
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The ratio between the largest and the smallest element is huge and that is \
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not good.\
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\>", "Text",ExpressionUUID->"de2e48d9-41ee-4790-884b-defce60aabf9"],
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Cell[BoxData[
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CellLabel->"In[8]:=",ExpressionUUID->"64c250ea-9085-4823-8744-99ce4dc4c345"],
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Cell["\<\
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Visualize resulting mesh. See uneven distribution of elements in some \
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particular regions.\
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\>", "Text",ExpressionUUID->"18fa2507-688d-4d5f-a1af-88eb1ed57c49"],
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Cell[BoxData[
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@@ -146,20 +165,30 @@ Cell[BoxData[
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RowBox[{"ImageSize", "\[Rule]", "300"}], ",", "\[IndentingNewLine]",
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Cell[CellGroupData[{
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Cell["Gmsh", "Subsubsection",ExpressionUUID->"a96e88eb-3367-4ecd-982c-8585a2e28f50"],
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Cell["Gmsh meshing method", \
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"Subsubsection",ExpressionUUID->"a96e88eb-3367-4ecd-982c-8585a2e28f50"],
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Cell["\<\
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This is basic method to define GMSH should be used as mesh generator.\
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\>", "Text",ExpressionUUID->"c01cb354-fa3c-4ef6-b4d3-b659aa2d2ae6"],
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Cell[BoxData[
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RowBox[{"mesh", "=",
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RowBox[{"reg", ",", "\[IndentingNewLine]",
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RowBox[{"\"\<BoundaryMeshGenerator\>\"", "\[Rule]", "None"}], ",",
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"\[IndentingNewLine]",
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CellLabel->"In[78]:=",ExpressionUUID->"b83f96fc-9491-4e94-b273-b53e9b5c332e"],
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CellLabel->"In[10]:=",ExpressionUUID->"b83f96fc-9491-4e94-b273-b53e9b5c332e"],
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Cell["Minimal element quality is much better.", \
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"Text",ExpressionUUID->"f2612389-a9ab-49d6-b436-e95e78c2e167"],
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Cell[BoxData[{
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RowBox[{
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RowBox[{
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CellLabel->"In[11]:=",ExpressionUUID->"41da77ad-b373-4637-9d33-983738c56895"],
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Cell["\<\
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Also the ratio between the largest and the smallest element is much better.\
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\>", "Text",ExpressionUUID->"5ad58e15-9176-4bbe-8004-a4e5b4f63c0a"],
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Cell[BoxData[
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Cell["\<\
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See the mesh with more uniform element size distribution and accurate \
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representation of boundaries.\
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\>", "Text",ExpressionUUID->"e6b6152d-cbad-401c-8f72-3df98f50cd21"],
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Cell[BoxData[
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}, Open ]],
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Cell[CellGroupData[{
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Cell["Options", "Subsubsection",ExpressionUUID->"105ed810-aaa6-4812-8974-47b492c6ab70"],
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Cell["Options of GmshGenerator", \
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Cell["See al available options of GmshGenerator function.", \
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"Text",ExpressionUUID->"26db999c-974e-440d-9e61-d3702791f747"],
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CellLabel->"In[83]:=",ExpressionUUID->"16201586-65a4-41fa-bcea-7bcb926e44c5"],
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CellLabel->"In[15]:=",ExpressionUUID->"16201586-65a4-41fa-bcea-7bcb926e44c5"],
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Cell["\<\
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Use some options to set mesh order to 2, larger element size (MaxCellMeasure) \
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and not particularly optimized element shape.\
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\>", "Text",ExpressionUUID->"5b608483-b6c5-41f3-8f56-6b93752ecdb7"],
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Cell[BoxData[
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Cell["\<\
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Visualize this coarse mesh. Note that mesh order is 2 and additional nodes \
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are present on tetrahedron edges.\
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\>", "Text",ExpressionUUID->"afab4048-ea8e-4d61-81c3-7d5cdf4170f2"],
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Cell[BoxData[
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WindowSize->{958, 1086},
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WindowMargins->{{Automatic, -8}, {Automatic, 0}},
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FrontEndVersion->"11.3 for Microsoft Windows (64-bit) (March 6, 2018)",
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PrivateNotebookOptions->{"FileOutlineCache"->False},
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FrontEndVersion->"12.0 for Microsoft Windows (64-bit) (April 8, 2019)",
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StyleDefinitions->"Default.nb"
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