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GmshLink

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).

Usage

Prerequisites

  • The latest release (4.0+) of open source meshing software Gmsh.
  • ImportMesh (0.3.2) 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.

 (* Load the package. *)
Get["GmshLink`"]

(* Set your path to Gmsh executable. *)
$GmshDirectory ="local/path/to/Gmsh.exe";

(* 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]

mesh["Wireframe"[
    "MeshElement" -> "MeshElements",
    "MeshElementStyle" -> FaceForm@LightBlue
]]

mesh