Hello,
I would like to use the NonMatching::QuadratureGenerator<dim> class
directly, as I need to generate multiple (as in many!, unfortunately)
nonmatching quadratures for the same cell. Therefore I would like to avoid
the route of interpolating the level set function onto the whole mesh etc,
as described in CutFEM tutorial.
Therefore I am thinking about calling the "generate" function, which only
needs a level set function and a bounding box as inputs. According to the
documentation the level set function should provide the gradient and the
Hessian. I would like to do this in the reference cell coordinates, so
that I can simply use this quadrature later via FEView as one normally does.
* The bounding box I presume is the hypercube [0,1]^{dim} for the meshes I
am interested in. (Can one request them for the reference cell and not the
triangulation cell?)
* The level set function should also be reasonably straightforward. I
know the function in the physical coordinates (say, f(x)) and all its
derivatives. I can also get the map from reference to physical coordinates
via FEView, let us call this map x=M(y). The issue is how to extract the
derivatives of this map so that the chain rule can be applied? I am mostly
working with Q1 maps, so of course I could figure out the derivatives "by
hand". I am just wondering if there is a more intelligent (code-wise) way
of doing this?
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