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bugs - Sometimes Region can't build right region


During my work with NDSolveFEM I found strange behavior of function Region.


a = 600;

reg1 = Rectangle[{0, 0}, {6 a, a}];
hole1 = Disk[{3 a, 0.75 a}, a/8];
hole2 = Disk[{3 a, 0.25 a}, a/8];
hole3 = Disk[{2.5 a, 0.5 a}, a/8];
resreg = RegionDifference[reg1, RegionUnion[hole1, hole2, hole3]]

So, it is really simple region with 3 holes near the centre of rectangle 6a * a.


resreg is:


BooleanRegion[#1 && ! (#2 || #3 || #4) &, {Rectangle[{0, 0}, 
{3600, 600}], Disk[{1800, 450.}, 75], Disk[{1800, 150.}, 75], Disk[{1500., 300.}, 75]}]


If I try to plot it by Region on my first computer, I will receive the simple Quad region 1 * 1: enter image description here


So, this region is unmeshable and I can't understand the reason of this behavior.


If I try it on my notebook. I will receive the right plot and meshable region. enter image description here


Mesh of region: enter image description here


Both computers have Windows 10 with Mathematica v 11.3. How I can make Region plot right image?



Answer



This is a bug and you should report it to support@wolfram.com. Here is why - simply because DiscretizeRegion has the same problem and does not give a message about it:


a = 600;
reg1 = Rectangle[{0, 0}, {6 a, a}];

hole1 = Disk[{3 a, 0.75 a}, a/8];
hole2 = Disk[{3 a, 0.25 a}, a/8];
hole3 = Disk[{2.5 a, 0.5 a}, a/8];
resreg = RegionDifference[reg1, RegionUnion[hole1, hole2, hole3]];

enter image description here


The finite element functions have the same problem, but they give a message about what is going on. Start with a fresh kernel:


Quit

And then:



a = 600;
reg1 = Rectangle[{0, 0}, {6 a, a}];
hole1 = Disk[{3 a, 0.75 a}, a/8];
hole2 = Disk[{3 a, 0.25 a}, a/8];
hole3 = Disk[{2.5 a, 0.5 a}, a/8];
resreg = RegionDifference[reg1, RegionUnion[hole1, hole2, hole3]];
NDSolve`FEM`ToElementMesh[resreg]

This gives a message:


enter image description here



So now we know that the RegionBounds computation either timed out or was not able to compute the bounds. However, when you call


RegionBounds[resreg]

You will get the bounds. Once the bounds are computed they are cached. That's why we needed the Quit above to make sure that we start from the same state.


As a workaround you can compute the RegionBounds before calling Region, or, if you happen to already have a FEM mesh just use:


 Region[MeshRegion[myFEMMesh]]

or


MeshRegion[myFEMMesh]

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