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craffael / lehrfempp

Simple Finite Element Framework for research and education
MIT License
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Adapt `lf::io` to support higher order polynomials #114

Open craffael opened 5 years ago

craffael commented 5 years ago

At the moment the function write_tikz outputs nodes of the mesh and connects them with straight line segments (codim=1 entities). I propose to add another option to WriteTikz named TikzOutputControl::SecondOrder which will connect the nodes using parabolas.

This functionality is mainly interesting for Geometry Elements that use second order (or higher) geometry approximation in which case the trias/quads can be represented exactly. But Implementing this functionality is not trivial because the Geometry interface doesn't provide us with the parametrization of the parabola directly. I propose to solve this problem as follows:

For every edge connecting two nodes we evaluate the edge geometry element at three points: at the two endpoints and at the point in the middle (average of the endpoints). We then construct a parabola that goes through these three points and give this parametrization to tikz.

anianruoss commented 5 years ago

I will implement the same functionality for lf::io::writeMatplotlib. As I am not very well versed in MATLAB, I think it would be easier if you extend lf::io::writeMatlab @hiptmair. What do you think?

hiptmair commented 5 years ago

I will take care of the MATLAB visualization tool, but only in the near future, because it will be an afternoon's work to implement and test everything.

craffael commented 5 years ago

I have seen that Paraview supports up to order 10 lagrangian elements since about a year. I will update the VTKWriter accordingly.