Dear developers and users,
I have two meshes one is immersed in the other. I wanted to find the
intersection between the two meshes, so I used the following function.
NonMatching::compute_intersection(omega_grid_tools_cache,
omega2_grid_tools_cache,
4, // degree
1e-20); // to
include header
<https://github.com/dealii/dealii/blob/master/include/deal.II/cgal/intersections.h>
source code
<https://github.com/dealii/dealii/blob/master/source/cgal/intersections.cc>
This function uses CGAL to find a quadrature formula to integrate exactly
on the intersection of two meshes which neglecte intersections of areas
with tolerance smaller than “tol“ that one chooses and gives a quadrature
formula on the triangulation of the intersection area that integrates
exactly polynomials of a specific degree ( which allows maximum degree of
4).
Say that I want to integrate, on the intersection area, a polynomial of
order 4.
I noticed that If I am considering a circular immersed domain (unlike
square or L-shaped domains), after a few cycles, the quadrature formula is
not accurate enough. To be precise, I find that the sum of the weights of
the quadrature formula defined on the triangulation of the exact
intersection of the two meshes does not sum up (up to a tolerance) to the
measure of the domain. When this occurs, the solution that is solved by
evaluating the integral considering the quadrature formula on the exact
intersection is no longer correct and the error starts to diverge in the
later cycles after this point.
Moreover, the difference gets large suddenly, in one cycle, the difference
was relatively smaller (1e-13), and in the next, it is much larger (1e-8)
as can be seen in the attached plot (Plot shows the difference between the
sum of the weights on the whole domain defined on the triangulation of the
exact intersection of the two meshes and the measure of the domain under
uniform refinement of the mesh).
Any suggestion on what could be the issue and what should I do to fix it?
Thanks
Najwa
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test_quad.pdf
Description: Adobe PDF document
