# [Gmsh] Meshing volumes with multiple inclusions

Philipp Metsch philipp.metsch at tu-dresden.de
Fri Aug 18 16:37:44 CEST 2017

```Hi everybody,

I have a problem with the mesh generation of a domain which
incorporates several inclusions that are allowed to intersect the
boundaries. The basic idea is to generate a periodic representative
volume element by using Boolean operations in Gmsh. So far, the
geometry generation seems to work quite well but when I try to mesh the
resulting geometry with Gmsh, I always get the error that there are
intersecting surfaces in the surface mesh. For this reason, the 3D mesh
is not completed. What do I do wrong? Does anybody have any ideas?

My .geo-file looks as follows (here only a simplified version with a
few inclusions):

// Number of inclusions
nInc=14;

// Geometrical tolerance
tol=Geometry.Tolerance;

// Mesh options
h=0.5;
p=1;

// Cuboid
Box(1) = {0, 0, 0, 10, 10, 10};

// Inclusions
Sphere(2) = {7.9403,3.8106,4.0937,2.5};
Sphere(3) = {-2.0597,3.8106,4.0937,2.5};
Sphere(4) = {3.1291,8.6325,8.5502,2.5};
Sphere(5) = {3.1291,-1.3675,8.5502,2.5};
Sphere(6) = {3.1291,8.6325,-1.4498,2.5};
Sphere(7) = {3.1291,-1.3675,-1.4498,2.5};
Sphere(8) = {8.9159,8.8189,5.2511,2.5};
Sphere(9) = {-1.0841,8.8189,5.2511,2.5};
Sphere(10) = {8.9159,-1.1811,5.2511,2.5};
Sphere(11) = {-1.0841,-1.1811,5.2511,2.5};
Sphere(12) = {9.9252,4.1353,9.0195,2.5};
Sphere(13) = {-0.074811,4.1353,9.0195,2.5};
Sphere(14) = {9.9252,4.1353,-0.98047,2.5};
Sphere(15) = {-0.074811,4.1353,-0.98047,2.5};

// Boolean Operations
Inclusions[]=BooleanIntersection{ Volume{1}; }{ Volume{2:nInc+1};
Delete;};
Matrix[]=BooleanDifference{ Volume{1}; Delete; }{ Volume{Inclusions[]};
};

// General Meshing Options
AllSurfs[] = Unique(Abs(Boundary{ Volume{Matrix[]};
Volume{Inclusions[]}; }));
AllLines[] = Unique(Abs(Boundary{ Surface{AllSurfs[]}; }));
AllPoints[] = Unique(Abs(Boundary{ Line{AllLines[]}; }));
Characteristic Length { AllPoints[] } = h;
Mesh.ElementOrder = p;

Mesh 3;
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```