I would like to perform local mesh refinement depending on physical results obtained with a prior simulation. I am using GMSH and the setSizeCallback(meshSizeCallBack) function to apply the desired mesh size in the refinement region. The obtained results are not the ones expected. I reproduce the issue on a simple example:
The 2 first columns of the data.csv file are the X and Y coordinates of the points that I want to modify. The 3rd column contains the desired mesh size. Note that this file has been truncated because of the text body character limit of the forum, but the issue is still repeatable with the fragment given below.
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0.88932 0.30017 0.33352
0.90086 0.30017 0.33636
0.91251 0.30017 0.33919
0.92429 0.30017 0.34479
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0.94818 0.30017 0.35032
0.96031 0.30017 0.35032
0.97256 0.30017 0.35577
0.98493 0.30017 0.35577
0.99743 0.30017 0.36115
1.01 0.30017 0.36115
1.0228 0.30017 0.36645
1.0357 0.30017 0.36645
1.0487 0.30017 0.36907
1.0618 0.30017 0.37167
1.0751 0.30017 0.37425
1.0885 0.30017 0.37681
1.102 0.30017 0.38188
1.1157 0.30017 0.38188
1.1295 0.30017 0.38687
1.1434 0.30017 0.38687
1.1575 0.30017 0.38934
1.1717 0.30017 0.39202
1.1861 0.30017 0.39202
1.2006 0.30017 0.39446
1.2152 0.30017 0.39929
1.23 0.30017 0.39929
1.245 0.30017 0.40168
1.2601 0.30017 0.40643
1.2753 0.30017 0.40643
1.2907 0.30017 0.40878
1.3063 0.30017 0.41343
1.322 0.30017 0.41343
1.3378 0.30017 0.42001
1.3539 0.30017 0.42001
1.3701 0.30017 0.42034
1.3864 0.30017 0.42262
1.4029 0.30017 0.42489
1.4196 0.30017 0.42715
1.4364 0.30017 0.4294
1.4534 0.30017 0.43165
1.4706 0.30017 0.43793
0.43702 0.3033 0.17856
0.44404 0.3033 0.17856
0.45112 0.3033 0.18117
0.45828 0.3033 0.1865
0.46551 0.3033 0.1865
0.47281 0.3033 0.19197
0.48019 0.3033 0.19197
0.48763 0.3033 0.19758
0.49516 0.3033 0.19758
0.50275 0.3033 0.20316
0.51043 0.3033 0.20907
0.51818 0.3033 0.20907
0.52601 0.3033 0.21515
0.53391 0.3033 0.21515
0.5419 0.3033 0.21825
0.54996 0.3033 0.22456
0.55811 0.3033 0.22456
0.56634 0.3033 0.23099
0.57465 0.3033 0.23099
0.58304 0.3033 0.23753
0.59152 0.3033 0.23753
0.60008 0.3033 0.24082
0.60872 0.3033 0.24413
0.61746 0.3033 0.24743
0.62628 0.3033 0.25073
0.63519 0.3033 0.25073
0.64419 0.3033 0.25723
0.65327 0.3033 0.25723
0.66245 0.3033 0.26048
0.67172 0.3033 0.26373
0.68109 0.3033 0.2702
0.69054 0.3033 0.2734
0.70009 0.3033 0.27975
0.70974 0.3033 0.27975
0.71949 0.3033 0.28288
0.72933 0.3033 0.28599
0.73927 0.3033 0.28908
0.7493 0.3033 0.29216
0.75944 0.3033 0.29522
0.76968 0.3033 0.29826
0.78003 0.3033 0.30431
0.79047 0.3033 0.30431
0.80103 0.3033 0.31031
0.81168 0.3033 0.31031
0.82244 0.3033 0.31624
0.83332 0.3033 0.31624
0.84429 0.3033 0.31918
0.85538 0.3033 0.32502
0.86658 0.3033 0.32502
0.8779 0.3033 0.32792
0.88932 0.3033 0.3308
0.90086 0.3033 0.33366
0.91251 0.3033 0.3339
0.92429 0.3033 0.33675
0.93618 0.3033 0.33959
0.94818 0.3033 0.3452
0.96031 0.3033 0.3452
0.97256 0.3033 0.34798
0.98493 0.3033 0.35074
0.99743 0.3033 0.35621
1.01 0.3033 0.35621
1.0228 0.3033 0.35891
1.0357 0.3033 0.36426
1.0487 0.3033 0.36426
1.0618 0.3033 0.36691
1.0751 0.3033 0.37214
1.0885 0.3033 0.37214
1.102 0.3033 0.3773
1.1157 0.3033 0.3773
1.1295 0.3033 0.38238
1.1434 0.3033 0.38238
1.1575 0.3033 0.38739
1.1717 0.3033 0.38739
1.1861 0.3033 0.39202
1.2006 0.3033 0.39446
1.2152 0.3033 0.39929
1.23 0.3033 0.39929
1.245 0.3033 0.40202
1.2601 0.3033 0.40202
1.2753 0.3033 0.40878
1.2907 0.3033 0.40878
1.3063 0.3033 0.41343
1.322 0.3033 0.41343
1.3378 0.3033 0.41613
1.3539 0.3033 0.41613
1.3701 0.3033 0.41844
1.3864 0.3033 0.42074
1.4029 0.3033 0.42531
1.4196 0.3033 0.42531
1.4364 0.3033 0.4294
1.4534 0.3033 0.43165
1.4706 0.3033 0.43211
1.488 0.3033 0.43436
1.5055 0.3033 0.43885
1.5232 0.3033 0.43885
0.37692 0.3064 0.15421
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0.38981 0.3064 0.15883
0.39636 0.3064 0.16119
0.40297 0.3064 0.16357
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0.41639 0.3064 0.16615
0.4232 0.3064 0.16862
0.43007 0.3064 0.17112
0.43702 0.3064 0.17365
0.44404 0.3064 0.17621
0.45112 0.3064 0.17881
0.45828 0.3064 0.18143
0.46551 0.3064 0.18409
0.47281 0.3064 0.18678
0.48019 0.3064 0.1895
0.48763 0.3064 0.19226
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0.50275 0.3064 0.20076
0.51043 0.3064 0.20076
0.51818 0.3064 0.20661
0.52601 0.3064 0.20661
0.53391 0.3064 0.20959
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0.54996 0.3064 0.21566
0.55811 0.3064 0.22186
0.56634 0.3064 0.22186
0.57465 0.3064 0.22819
0.58304 0.3064 0.22819
0.59152 0.3064 0.2346
0.60008 0.3064 0.2346
0.60872 0.3064 0.24106
0.61746 0.3064 0.24106
0.62628 0.3064 0.25073
0.63519 0.3064 0.25073
0.64419 0.3064 0.25081
0.65327 0.3064 0.25406
0.66245 0.3064 0.26058
0.67172 0.3064 0.26058
0.68109 0.3064 0.26709
0.69054 0.3064 0.26709
0.70009 0.3064 0.27357
0.70974 0.3064 0.27357
0.71949 0.3064 0.27999
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0.85538 0.3064 0.31969
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0.8779 0.3064 0.32815
0.88932 0.3064 0.32815
0.90086 0.3064 0.3339
0.91251 0.3064 0.3339
0.92429 0.3064 0.33675
0.93618 0.3064 0.33959
0.94818 0.3064 0.3452
0.96031 0.3064 0.3452
0.97256 0.3064 0.34798
0.98493 0.3064 0.35074
0.99743 0.3064 0.35621
1.01 0.3064 0.35621
1.0228 0.3064 0.35891
1.0357 0.3064 0.36426
1.0487 0.3064 0.36426
1.0618 0.3064 0.3646
1.0751 0.3064 0.37214
1.0885 0.3064 0.37214
1.102 0.3064 0.37508
1.1157 0.3064 0.37508
1.1295 0.3064 0.38021
1.1434 0.3064 0.38021
1.1575 0.3064 0.38526
1.1717 0.3064 0.38526
1.1861 0.3064 0.38987
1.2006 0.3064 0.39233
1.2152 0.3064 0.39721
1.23 0.3064 0.39721
1.245 0.3064 0.40202
1.2601 0.3064 0.40202
1.2753 0.3064 0.40441
1.2907 0.3064 0.40913
1.3063 0.3064 0.40913
1.322 0.3064 0.41148
1.3378 0.3064 0.41613
1.3539 0.3064 0.41613
1.3701 0.3064 0.41844
1.3864 0.3064 0.42074
1.4029 0.3064 0.42531
1.4196 0.3064 0.42531
1.4364 0.3064 0.42808
1.4534 0.3064 0.42808
1.4706 0.3064 0.43211
1.488 0.3064 0.43263
1.5055 0.3064 0.43489
1.5232 0.3064 0.43715
1.5411 0.3064 0.44166
1.5591 0.3064 0.44166
The GMSH code run with Python API is given below:
import gmsh
import numpy as np
from scipy.interpolate import NearestNDInterpolator
import matplotlib.pyplot as plt
import numpy
import csv
def meshSizeCallback(dim, tag, x, y, z, lc):
return min(lc, background_field(x,y))
gmsh.initialize()
lc=0.2
gmsh.option.setNumber("Mesh.CharacteristicLengthMax", lc)
# Building the geometry
gmsh.model.occ.addPoint(0,0,0,lc)
gmsh.model.occ.addPoint(0,0.5,0,lc)
gmsh.model.occ.addPoint(3,0.5,0,lc)
gmsh.model.occ.addPoint(3,0,0,lc)
gmsh.model.occ.addLine(1,2)
gmsh.model.occ.addLine(2,3)
gmsh.model.occ.addLine(3,4)
gmsh.model.occ.addLine(4,1)
gmsh.model.occ.addCurveLoop([1,2,3,4],1)
gmsh.model.occ.addPlaneSurface([1],2)
gmsh.model.occ.synchronize()
# Reading the data.csv file containing the point coordinates as well as the desired cell size
background_field = []
with open('coord_regions_int_maillage_B_threshold_14_maj_Delta_2D.csv','r',encoding="utf8", errors='ignore') as csvfile:
points = csv.reader(csvfile, delimiter = ',')
for [x,y,ls] in points: # for each point in the csv file
background_field.append([float(x), float(y), float(ls)/10]) #the mesh size is divided by 10 in order to clearly separate the refinement region from the rest of the mesh
background_field = np.array(background_field)
X = background_field[:,0]
Y = background_field[:,1]
# Interpolating the background field (required for the call back function)
background_field = NearestNDInterpolator(background_field[:,0:2], background_field[:,2]) # First input: point coordinates, Second input: value
gmsh.model.mesh.setSizeCallback(meshSizeCallback) # Keep the minimum cell size between the background and the intial mesh size
# Generating 2D mesh
gmsh.model.mesh.generate(2)
# Writing the mesh
gmsh.write("maillage_auto.msh")
gmsh.fltk.run()
gmsh.finalize()
# Plot the surface in Python to compare with the GMSH results
plt.scatter(X, Y, c=background_field(X,Y))
plt.xlabel("X")
plt.ylabel("Y")
plt.colorbar()
plt.show()
Unfortunately, the refined area obtained with GMSH is different from the refined area given by the background_field (see attached pictures). May someone help me to understand why the refined area obtained in GMSH does not correspond with the region described in data.csv? Moreover, the mesh size is the non refined region is smaller than the prescribed mesh size lc=0.2. What is the reason for this result ?
Thanks a lot for your answer!
