Tutorial 5
Mesh sizes, holes in volumes
import gmshgmsh.initialize()gmsh.model.add("t5")lcar1 = .1
lcar2 = .0005
lcar3 = .0550.055If we wanted to change these mesh sizes globally (without changing the above definitions), we could give a global scaling factor for all mesh sizes with e.g.
gmsh.option.setNumber("Mesh.MeshSizeFactor", 0.1); See Tutorial 10 for more information about mesh sizes.
We proceed by defining some elementary entities describing a truncated cube:
gmsh.model.geo.addPoint(0.5,0.5,0.5, lcar2, 1)
gmsh.model.geo.addPoint(0.5,0.5,0, lcar1, 2)
gmsh.model.geo.addPoint(0,0.5,0.5, lcar1, 3)
gmsh.model.geo.addPoint(0,0,0.5, lcar1, 4)
gmsh.model.geo.addPoint(0.5,0,0.5, lcar1, 5)
gmsh.model.geo.addPoint(0.5,0,0, lcar1, 6)
gmsh.model.geo.addPoint(0,0.5,0, lcar1, 7)
gmsh.model.geo.addPoint(0,1,0, lcar1, 8)
gmsh.model.geo.addPoint(1,1,0, lcar1, 9)
gmsh.model.geo.addPoint(0,0,1, lcar1, 10)
gmsh.model.geo.addPoint(0,1,1, lcar1, 11)
gmsh.model.geo.addPoint(1,1,1, lcar1, 12)
gmsh.model.geo.addPoint(1,0,1, lcar1, 13)
gmsh.model.geo.addPoint(1,0,0, lcar1, 14)14gmsh.model.geo.addLine(8,9, 1); gmsh.model.geo.addLine(9,12, 2)
gmsh.model.geo.addLine(12,11, 3); gmsh.model.geo.addLine(11,8, 4)
gmsh.model.geo.addLine(9,14, 5); gmsh.model.geo.addLine(14,13, 6)
gmsh.model.geo.addLine(13,12, 7); gmsh.model.geo.addLine(11,10, 8)
gmsh.model.geo.addLine(10,13, 9); gmsh.model.geo.addLine(10,4, 10)
gmsh.model.geo.addLine(4,5, 11); gmsh.model.geo.addLine(5,6, 12)
gmsh.model.geo.addLine(6,2, 13); gmsh.model.geo.addLine(2,1, 14)
gmsh.model.geo.addLine(1,3, 15); gmsh.model.geo.addLine(3,7, 16)
gmsh.model.geo.addLine(7,2, 17); gmsh.model.geo.addLine(3,4, 18)
gmsh.model.geo.addLine(5,1, 19); gmsh.model.geo.addLine(7,8, 20)
gmsh.model.geo.addLine(6,14, 21);gmsh.model.geo.addCurveLoop([-11,-19,-15,-18], 22)
gmsh.model.geo.addPlaneSurface([22], 23)
gmsh.model.geo.addCurveLoop([16,17,14,15], 24)
gmsh.model.geo.addPlaneSurface([24], 25)
gmsh.model.geo.addCurveLoop([-17,20,1,5,-21,13], 26)
gmsh.model.geo.addPlaneSurface([26], 27)
gmsh.model.geo.addCurveLoop([-4,-1,-2,-3], 28)
gmsh.model.geo.addPlaneSurface([28], 29)
gmsh.model.geo.addCurveLoop([-7,2,-5,-6], 30)
gmsh.model.geo.addPlaneSurface([30], 31)
gmsh.model.geo.addCurveLoop([6,-9,10,11,12,21], 32)
gmsh.model.geo.addPlaneSurface([32], 33)
gmsh.model.geo.addCurveLoop([7,3,8,9], 34)
gmsh.model.geo.addPlaneSurface([34], 35)
gmsh.model.geo.addCurveLoop([-10,18,-16,-20,4,-8], 36)
gmsh.model.geo.addPlaneSurface([36], 37)
gmsh.model.geo.addCurveLoop([-14,-13,-12,19], 38)
gmsh.model.geo.addPlaneSurface([38], 39)39shells = []Any[]sl = gmsh.model.geo.addSurfaceLoop([35,31,29,37,33,23,39,25,27])
push!(shells, sl)1-element Array{Any,1}:
1This function will create a spherical hole in a volume. We don't specify tags manually, and let the functions return them automatically:
function cheeseHole(x, y, z, r, lc, shells)
p1 = gmsh.model.geo.addPoint(x, y, z, lc)
p2 = gmsh.model.geo.addPoint(x+r,y, z, lc)
p3 = gmsh.model.geo.addPoint(x, y+r,z, lc)
p4 = gmsh.model.geo.addPoint(x, y, z+r, lc)
p5 = gmsh.model.geo.addPoint(x-r,y, z, lc)
p6 = gmsh.model.geo.addPoint(x, y-r,z, lc)
p7 = gmsh.model.geo.addPoint(x, y, z-r, lc)
c1 = gmsh.model.geo.addCircleArc(p2,p1,p7)
c2 = gmsh.model.geo.addCircleArc(p7,p1,p5)
c3 = gmsh.model.geo.addCircleArc(p5,p1,p4)
c4 = gmsh.model.geo.addCircleArc(p4,p1,p2)
c5 = gmsh.model.geo.addCircleArc(p2,p1,p3)
c6 = gmsh.model.geo.addCircleArc(p3,p1,p5)
c7 = gmsh.model.geo.addCircleArc(p5,p1,p6)
c8 = gmsh.model.geo.addCircleArc(p6,p1,p2)
c9 = gmsh.model.geo.addCircleArc(p7,p1,p3)
c10 = gmsh.model.geo.addCircleArc(p3,p1,p4)
c11 = gmsh.model.geo.addCircleArc(p4,p1,p6)
c12 = gmsh.model.geo.addCircleArc(p6,p1,p7)
l1 = gmsh.model.geo.addCurveLoop([c5,c10,c4])
l2 = gmsh.model.geo.addCurveLoop([c9,-c5,c1])
l3 = gmsh.model.geo.addCurveLoop([c12,-c8,-c1])
l4 = gmsh.model.geo.addCurveLoop([c8,-c4,c11])
l5 = gmsh.model.geo.addCurveLoop([-c10,c6,c3])
l6 = gmsh.model.geo.addCurveLoop([-c11,-c3,c7])
l7 = gmsh.model.geo.addCurveLoop([-c2,-c7,-c12])
l8 = gmsh.model.geo.addCurveLoop([-c6,-c9,c2])
s1 = gmsh.model.geo.addSurfaceFilling([l1])
s2 = gmsh.model.geo.addSurfaceFilling([l2])
s3 = gmsh.model.geo.addSurfaceFilling([l3])
s4 = gmsh.model.geo.addSurfaceFilling([l4])
s5 = gmsh.model.geo.addSurfaceFilling([l5])
s6 = gmsh.model.geo.addSurfaceFilling([l6])
s7 = gmsh.model.geo.addSurfaceFilling([l7])
s8 = gmsh.model.geo.addSurfaceFilling([l8])
sl = gmsh.model.geo.addSurfaceLoop([s1, s2, s3, s4, s5, s6, s7, s8])
v = gmsh.model.geo.addVolume([sl])
push!(shells, sl)
return v
endcheeseHole (generic function with 1 method)We create five holes in the cube:
x = 0
y = 0.75; z = 0; r = 0.09
for t in 1:5
global x, z
x += 0.166
z += 0.166
v = cheeseHole(x, y, z, r, lcar3, shells)
gmsh.model.geo.addPhysicalGroup(3, [v], t)
endThe volume of the cube, without the 5 holes, is defined by 6 surface loops: the first surface loop defines the exterior surface; the surface loops other than the first one define holes:
gmsh.model.geo.addVolume(shells, 186);gmsh.model.geo.synchronize()We finally define a physical volume for the elements discretizing the cube, without the holes (for which physical groups were already defined in the cheeseHole() function):
gmsh.model.addPhysicalGroup(3, [186], 10);To generate a curvilinear mesh and optimize it to produce provably valid curved elements (see A. Johnen, J.-F. Remacle and C. Geuzaine. Geometric validity of curvilinear finite elements. Journal of Computational Physics 233, pp. 359-372, 2013; and T. Toulorge, C. Geuzaine, J.-F. Remacle, J. Lambrechts. Robust untangling of curvilinear meshes. Journal of Computational Physics 254, pp. 8-26, 2013), you can uncomment the following lines:
gmsh.option.setNumber("Mesh.ElementOrder", 2) gmsh.option.setNumber("Mesh.HighOrderOptimize", 2)
gmsh.model.mesh.generate(3)
gmsh.write("t5.msh")Info : Meshing 1D...
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Info : Done meshing 1D (Wall 0.0188515s, CPU 0.018844s)
Info : Meshing 2D...
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Info : Done meshing 2D (Wall 0.05538s, CPU 0.055377s)
Info : Meshing 3D...
Info : 3D Meshing 6 volumes with 1 connected component
Info : Tetrahedrizing 1535 nodes...
Info : Done tetrahedrizing 1543 nodes (Wall 0.0204541s, CPU 0.020451s)
Info : Reconstructing mesh...
Info : - Creating surface mesh
Info : - Identifying boundary edges
Info : - Recovering boundary
Info : Done reconstructing mesh (Wall 0.041124s, CPU 0.04112s)
Info : Found volume 186
Info : Found volume 3
Info : Found volume 2
Info : Found volume 4
Info : Found volume 1
Info : Found volume 5
Info : It. 0 - 0 nodes created - worst tet radius 15.1729 (nodes removed 0 0)
Info : It. 500 - 491 nodes created - worst tet radius 1.41358 (nodes removed 0 9)
Info : It. 1000 - 990 nodes created - worst tet radius 1.1124 (nodes removed 0 10)
Info : 3D refinement terminated (2890 nodes total):
Info : - 0 Delaunay cavities modified for star shapeness
Info : - 10 nodes could not be inserted
Info : - 13936 tetrahedra created in 0.0760767 sec. (183183 tets/s)
Info : Done meshing 3D (Wall 0.16183s, CPU 0.16181s)
Info : Optimizing mesh...
Info : Optimizing volume 1
Info : Optimization starts (volume = 0.00272564) with worst = 0.499334 / average = 0.670617:
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 2 elements
Info : 0.50 < quality < 0.60 : 15 elements
Info : 0.60 < quality < 0.70 : 57 elements
Info : 0.70 < quality < 0.80 : 36 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : No ill-shaped tets in the mesh :-)
Info : 0.00 < quality < 0.10 : 0 elements
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Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
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Info : 0.50 < quality < 0.60 : 15 elements
Info : 0.60 < quality < 0.70 : 57 elements
Info : 0.70 < quality < 0.80 : 36 elements
Info : 0.80 < quality < 0.90 : 0 elements
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Info : Optimizing volume 2
Info : Optimization starts (volume = 0.00272581) with worst = 0.504447 / average = 0.670923:
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 0 elements
Info : 0.50 < quality < 0.60 : 17 elements
Info : 0.60 < quality < 0.70 : 56 elements
Info : 0.70 < quality < 0.80 : 37 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : No ill-shaped tets in the mesh :-)
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 0 elements
Info : 0.50 < quality < 0.60 : 17 elements
Info : 0.60 < quality < 0.70 : 56 elements
Info : 0.70 < quality < 0.80 : 37 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : Optimizing volume 3
Info : Optimization starts (volume = 0.002728) with worst = 0.499334 / average = 0.664608:
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 2 elements
Info : 0.50 < quality < 0.60 : 18 elements
Info : 0.60 < quality < 0.70 : 57 elements
Info : 0.70 < quality < 0.80 : 35 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : No ill-shaped tets in the mesh :-)
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 2 elements
Info : 0.50 < quality < 0.60 : 18 elements
Info : 0.60 < quality < 0.70 : 57 elements
Info : 0.70 < quality < 0.80 : 35 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : Optimizing volume 4
Info : Optimization starts (volume = 0.00272865) with worst = 0.499334 / average = 0.665029:
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 2 elements
Info : 0.50 < quality < 0.60 : 18 elements
Info : 0.60 < quality < 0.70 : 57 elements
Info : 0.70 < quality < 0.80 : 35 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : No ill-shaped tets in the mesh :-)
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 2 elements
Info : 0.50 < quality < 0.60 : 18 elements
Info : 0.60 < quality < 0.70 : 57 elements
Info : 0.70 < quality < 0.80 : 35 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : Optimizing volume 5
Info : Optimization starts (volume = 0.00272218) with worst = 0.499334 / average = 0.676226:
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 2 elements
Info : 0.50 < quality < 0.60 : 10 elements
Info : 0.60 < quality < 0.70 : 59 elements
Info : 0.70 < quality < 0.80 : 37 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : No ill-shaped tets in the mesh :-)
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 0 elements
Info : 0.30 < quality < 0.40 : 0 elements
Info : 0.40 < quality < 0.50 : 2 elements
Info : 0.50 < quality < 0.60 : 10 elements
Info : 0.60 < quality < 0.70 : 59 elements
Info : 0.70 < quality < 0.80 : 37 elements
Info : 0.80 < quality < 0.90 : 0 elements
Info : 0.90 < quality < 1.00 : 0 elements
Info : Optimizing volume 186
Info : Optimization starts (volume = 0.86137) with worst = 0.0111303 / average = 0.737256:
Info : 0.00 < quality < 0.10 : 55 elements
Info : 0.10 < quality < 0.20 : 85 elements
Info : 0.20 < quality < 0.30 : 169 elements
Info : 0.30 < quality < 0.40 : 269 elements
Info : 0.40 < quality < 0.50 : 466 elements
Info : 0.50 < quality < 0.60 : 1281 elements
Info : 0.60 < quality < 0.70 : 2243 elements
Info : 0.70 < quality < 0.80 : 3256 elements
Info : 0.80 < quality < 0.90 : 3737 elements
Info : 0.90 < quality < 1.00 : 1821 elements
Info : 301 edge swaps, 8 node relocations (volume = 0.86137): worst = 0.299852 / average = 0.750443 (Wall 0.00562828s, CPU 0.005628s)
Info : No ill-shaped tets in the mesh :-)
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 0 elements
Info : 0.20 < quality < 0.30 : 1 elements
Info : 0.30 < quality < 0.40 : 262 elements
Info : 0.40 < quality < 0.50 : 470 elements
Info : 0.50 < quality < 0.60 : 1268 elements
Info : 0.60 < quality < 0.70 : 2255 elements
Info : 0.70 < quality < 0.80 : 3283 elements
Info : 0.80 < quality < 0.90 : 3783 elements
Info : 0.90 < quality < 1.00 : 1796 elements
Info : Done optimizing mesh (Wall 0.0189858s, CPU 0.018985s)
Info : 2895 nodes 17163 elements
Info : Writing 't5.msh'...
Info : Done writing 't5.msh'gmsh.finalize()This page was generated using Literate.jl.