Meshing bug: misidentification of overlapping edges

[cmdoug]

I believe there is a bug somewhere in the BAMG code used to identify overlapping edges (and also in the mortar construction). Below is a simple reproducer that is pretty contrived, but I have found this issue on other meshes with small clearances, especially when using adaptmesh(). I have looked into the bamg source code to find the issue, but the code and comments are difficult to understand... Does anyone with more familiarity with bamg have ideas for a fix?

real n0 = 64;
real n1 = 16;
real R = 1.0;
real L = 2*R;
real H = 2*R;
real h = 1.0e-4;

// Define borders
//  o-------4-------o
//  5               |
//  o--6--o         |
//         7        3
//  o---8---o       |
//  1               |
//  o-------2-------o
border C01(t=0, 1){x=-R; y=R*(1-t); label=1;}
border C02(t=0, 1){x=-R+L*t; y=0; label=2;}
border C03(t=0, 1){x=L-R; y=H*t; label=3;}
border C04(t=0, 1){x=L*(1-t)-R; y=H; label=4;}
border C05(t=0, 1){x=-R; y=H-(H-R-h)*t; label=5;}
border C06(t=0, 1){x=-R+(R-0.05)*t; y=R+h; label=6;}
border C07(t=0, 1){x=-0.05*(1-t); y=R+h*(1-t); label=7;}
border C08(t=0, 1){x=-R*t; y=R; label=8;}
// Assemble mesh
mesh Thg = buildmesh(C01(n0*R) + C02(n1*L) + C03(n1*H) + C04(n1*L) + C05(n1*(H-R-h)) + C06(n1*(R-0.05)) + C07(n0*sqrt(0.05^2+h^2)) + C08(n0*R));

[prj-]

@frederichecht, could you please have a look at this bug?

[frederichecht]

The problem is simple
you try to put a edge between 2 // edges with distance 1e-4 so the reache the eps limit of the mesh generator (bamg).
it is ok with 1e-3

[cmdoug]

Hi @frederichecht. Yes, I understand that. But (1) is there any reason why this limit is absolute instead of relative? And (2) why the limit is so strict? 1e-4 seems huge compared to floating point error in double precision with O(1) mesh diameters.

[frederichecht]

You can see the problem with a zoom (here h=1e-3) the problem two points are very close
see:

[cmdoug]

Yes, I understand. This is the purpose of my MWE. These points are close to each other but they are quite far compared to machine epsilon. My issue is that I cannot see why BAMG should trigger an error when we are so far from the floating point limit. I occasionally work on meshes that have such small gaps and cannot use FreeFEM for them because of this limitation. Is it possible to widen the error tolerances to accommodate such small clearances?

[cmdoug]

I believe such a change would involve modifications to hard-coded tolerances both in the BAMG code (e.g. src/bamglib/Mesh2.cpp, but also in, for example: src/femlib/fem.cpp for mortar construction.