GmshLink is a Mathematica package to create ElementMesh
objects via Gmsh meshing software.
It creates tetrahedral mesh with much better quality than built-in meshing algorithm.
Currently it works only for 3D symbolic regions obtained by boolean operations on
basic geometric primitives (Cuboid, Ball, Cylinder and Cone).
- The latest release (4.0+) of open source meshing software Gmsh.
- ImportMesh (0.3.3) package to import .msh files to Mathematica.
Gmsh doesn't require installation, just unzip it to any local directory.
Then copy the GmshLink.wl file to your local path FileNameJoin[{$UserBaseDirectory, "Applications"}] and
you can already try the following example in Mathematica notebook.
See Examples.nb notebook for more examples on how to use additional options of GmshGenerator function.
(* Load the package. *)
Get["GmshLink`"]
(* Set path directory containing Gmsh executable. *)
$GmshDirectory ="local/path/to/gmsh-4.4.1-Windows64";
(* Define symbolic region based on boolean operations with geometric primitives. *)
reg = RegionDifference[
RegionUnion@{
Ball[{0, 0, 0}, 1],
Ball[{1, 0, 0}, 4/5],
Ball[{9/5, 0, 0}, 3/5],
Ball[{12/5, 0, 0}, 2/5]
},
Cuboid[{-2, -2, 0}, {5, 2, 2}]
]
(* Create ElementMesh object from symbolic region. *)
mesh = ToElementMesh[reg,"ElementMeshGenerator" -> GmshGenerator]
(* Visualize the mesh with nice element distribution and accurate boundary representation. *)
mesh["Wireframe"[
"MeshElement" -> "MeshElements",
"MeshElementStyle" -> FaceForm@LightBlue
]]