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Gmsh Reference Manual the Documentation for Gmsh 4.8.0 a Finite Element Mesh Generator with Built-In Pre- and Post-Processing Facilities

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Gmsh Reference Manual the Documentation for Gmsh 4.8.0 a Finite Element Mesh Generator with Built-In Pre- and Post-Processing Facilities Gmsh Gmsh Reference Manual The documentation for Gmsh 4.8.0 A finite element mesh generator with built-in pre- and post-processing facilities 2 March 2021 Christophe Geuzaine Jean-Fran¸coisRemacle Copyright c 1997-2021 Christophe Geuzaine, Jean-Fran¸coisRemacle Permission is granted to make and distribute verbatim copies of this manual provided the copy- right notice and this permission notice are preserved on all copies. i Short Contents Obtaining Gmsh :::::::::::::::::::::::::::::::::::::::::::::::::::::::: 1 Copying conditions :::::::::::::::::::::::::::::::::::::::::::::::::::::: 3 1 Overview ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 5 2 How to read this reference manual? ::::::::::::::::::::::::::::::::::::: 9 3 Running Gmsh on your system :::::::::::::::::::::::::::::::::::::::: 11 4 General tools::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21 5 Geometry module ::::::::::::::::::::::::::::::::::::::::::::::::::: 35 6 Mesh module::::::::::::::::::::::::::::::::::::::::::::::::::::::: 45 7 Solver module :::::::::::::::::::::::::::::::::::::::::::::::::::::: 71 8 Post-processing module :::::::::::::::::::::::::::::::::::::::::::::: 73 9 File formats::::::::::::::::::::::::::::::::::::::::::::::::::::::: 105 A Tutorial :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 127 B Options :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 169 C Compiling the source code ::::::::::::::::::::::::::::::::::::::::::: 245 D Gmsh API :::::::::::::::::::::::::::::::::::::::::::::::::::::::: 249 E Information for developers ::::::::::::::::::::::::::::::::::::::::::: 329 F Frequently asked questions::::::::::::::::::::::::::::::::::::::::::: 331 G Version history :::::::::::::::::::::::::::::::::::::::::::::::::::: 339 H Copyright and credits ::::::::::::::::::::::::::::::::::::::::::::::: 353 I License::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 357 Concept index :::::::::::::::::::::::::::::::::::::::::::::::::::::::: 363 Syntax index:::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 365 iii Table of Contents Obtaining Gmsh ::::::::::::::::::::::::::::::::::::::::::::::::::: 1 Copying conditions :::::::::::::::::::::::::::::::::::::::::::::::: 3 1 Overview ::::::::::::::::::::::::::::::::::::::::::::::::::::::: 5 1.1 Geometry: model entity creation::::::::::::::::::::::::::::::::::::::::::::::::::: 5 1.2 Mesh: finite element mesh generation :::::::::::::::::::::::::::::::::::::::::::::: 5 1.3 Solver: external solver interface :::::::::::::::::::::::::::::::::::::::::::::::::::: 6 1.4 Post-processing: scalar, vector and tensor field visualization :::::::::::::::::::::::: 6 1.5 What Gmsh is pretty good at . ::::::::::::::::::::::::::::::::::::::::::::::::: 6 1.6 . and what Gmsh is not so good at :::::::::::::::::::::::::::::::::::::::::::::: 7 1.7 Bug reports ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 7 2 How to read this reference manual? ::::::::::::::::::::::::: 9 2.1 Syntactic rules used in the manual ::::::::::::::::::::::::::::::::::::::::::::::::: 9 3 Running Gmsh on your system ::::::::::::::::::::::::::::: 11 3.1 Interactive mode ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 11 3.2 Non-interactive mode::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 12 3.3 Command-line options:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 12 3.4 Mouse actions :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 16 3.5 Keyboard shortcuts :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 16 4 General tools ::::::::::::::::::::::::::::::::::::::::::::::::: 21 4.1 Comments ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21 4.2 Expressions :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21 4.2.1 Floating point expressions ::::::::::::::::::::::::::::::::::::::::::::::::::: 21 4.2.2 Character expressions:::::::::::::::::::::::::::::::::::::::::::::::::::::::: 23 4.2.3 Color expressions :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25 4.3 Operators :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25 4.4 Built-in functions::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 26 4.5 User-defined macros :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 28 4.6 Loops and conditionals ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 28 4.7 General commands ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 29 4.8 General options :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 33 5 Geometry module :::::::::::::::::::::::::::::::::::::::::::: 35 5.1 Geometry commands ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 35 5.1.1 Points ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 35 5.1.2 Curves :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36 5.1.3 Surfaces ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 37 5.1.4 Volumes ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 38 5.1.5 Extrusions::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 39 5.1.6 Boolean operations :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 41 5.1.7 Transformations ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 42 5.1.8 Miscellaneous:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43 5.2 Geometry options :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 44 iv Gmsh 4.8.0 6 Mesh module ::::::::::::::::::::::::::::::::::::::::::::::::: 45 6.1 Choosing the right unstructured algorithm :::::::::::::::::::::::::::::::::::::::: 45 6.2 Elementary entities vs. physical groups ::::::::::::::::::::::::::::::::::::::::::: 46 6.3 Mesh commands ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 47 6.3.1 Specifying mesh element sizes :::::::::::::::::::::::::::::::::::::::::::::::: 47 6.3.2 Structured grids ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 63 6.3.3 Miscellaneous:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 66 6.4 Mesh options ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 69 7 Solver module :::::::::::::::::::::::::::::::::::::::::::::::: 71 8 Post-processing module :::::::::::::::::::::::::::::::::::::: 73 8.1 Post-processing commands ::::::::::::::::::::::::::::::::::::::::::::::::::::::: 73 8.2 Post-processing plugins ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 77 8.3 Post-processing options:::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 103 9 File formats ::::::::::::::::::::::::::::::::::::::::::::::::: 105 9.1 MSH file format ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 105 9.2 Node ordering::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 112 9.2.1 Low order elements::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 112 9.2.2 High-order elements :::::::::::::::::::::::::::::::::::::::::::::::::::::::: 114 9.3 Legacy formats:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 114 9.3.1 MSH file format version 2 (Legacy) ::::::::::::::::::::::::::::::::::::::::: 115 9.3.2 MSH file format version 1 (Legacy) ::::::::::::::::::::::::::::::::::::::::: 120 9.3.3 POS ASCII file format (Legacy) :::::::::::::::::::::::::::::::::::::::::::: 121 9.3.4 POS binary file format (Legacy) :::::::::::::::::::::::::::::::::::::::::::: 124 Appendix A Tutorial ::::::::::::::::::::::::::::::::::::::::: 127 A.1 t1: Geometry basics, elementary entities, physical groups ::::::::::::::::::::::: 127 A.2 t2: Transformations, extruded geometries, volumes:::::::::::::::::::::::::::::: 129 A.3 t3: Extruded meshes, ONELAB parameters, options :::::::::::::::::::::::::::: 131 A.4 t4: Built-in functions, holes in surfaces, annotations, entity colors ::::::::::::::: 133 A.5 t5: Mesh sizes, macros, loops, holes in volumes:::::::::::::::::::::::::::::::::: 135 A.6 t6: Transfinite meshes :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 138 A.7 t7: Background meshes ::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 139 A.8 t8: Post-processing and animations ::::::::::::::::::::::::::::::::::::::::::::: 140 A.9 t9: Plugins ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 143 A.10 t10: Mesh size fields::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 144 A.11 t11: Unstructured quadrangular meshes ::::::::::::::::::::::::::::::::::::::: 145 A.12 t12: Cross-patch meshing with compounds::::::::::::::::::::::::::::::::::::: 147 A.13 t13: Remeshing an STL file without an underlying CAD model :::::::::::::::: 148 A.14 t14: Homology and cohomology computation :::::::::::::::::::::::::::::::::: 149 A.15 t15: Embedded points, lines and surfaces :::::::::::::::::::::::::::::::::::::: 150 A.16 t16: Constructive Solid Geometry, OpenCASCADE geometry kernel ::::::::::: 151 A.17 t17: Anisotropic background mesh::::::::::::::::::::::::::::::::::::::::::::: 153 A.18 t18: Periodic meshes :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 153 A.19 t19: Thrusections, fillets, pipes, mesh size from curvature :::::::::::::::::::::: 155 A.20 t20: STEP import and manipulation, geometry partitioning:::::::::::::::::::: 156 A.21 t21: Mesh partitioning :::::::::::::::::::::::::::::::::::::::::::::::::::::::: 157 A.22 x1: Geometry and mesh data :::::::::::::::::::::::::::::::::::::::::::::::::: 159 A.23 x2: Mesh import, discrete entities,
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