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Draft: MicroMesh & iso-/super-/sub-parametric elements
This MR introduces utilities to work with iso-, sub-, and super-parametric meshes.
Mainly it enables/simplifies working with meshes the node-positions of which are specified as finite element functions.
Instead of using the blending function feature, the geometry can be interpolated into a (vector-valued) P1 or P2 space.
Using the HOG, the local Jacobians can be computed straightforwardly by evaluation of the gradients of the shape functions (see hog!24 (merged)).
Functions to generate appropriate volume meshes from either surface meshes or analytical descriptions of curved geometries are not yet included in this MR.
For more details see docstring of MicroMesh.
Concrete changes
MicroMesh class and several centralized functions to compute node positions
corresponding VTK output adaptions
some tests
TODOs
Necessary
generate isoparametric operators necessary for the tests and update hyteg-operators afterwards
proper VTK test before merging this (specifically, #278 (closed) would be very nice)
Nice to have / next steps
proper, stable mesh improvement
semi-automated meshing from surface representations (e.g., via OpenMesh or gmsh)
tutorial
more operators
Images
2D, piecewise quadratic mesh (P2, level 3)
(left: coarse mesh, middle: projected, right: projected and corrected with diffusion)
3D, piecewise quadratic mesh (P2, level 3)
(left: coarse mesh, middle: projected, right: projected with edges)
