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Remark regarding sheet 8, programming exercise 9
Written on 09.12.2025 14:16 by Ruben Gutendorf
Dear students,
in order to solve the Neumann problem, you may wish to compute the outward-pointing normal of your triangles. You can compute this via rotation and normalisation if you know a priori the orientation of your triangles, but if not, this becomes a complicated and error-prone task - you would need to check if your normal points into or out of the triangle. In your code, the orientation of a polygon corresponds to the order of its edges in the element-node-table (counter-clockwise is "normal"). The only chance to know this orientation a priori is to check the orientation of the initial mesh and to make sure that your refinement routine preserves that initial orientation. You can verify this by plotting a constant with plot_trisurf without a colormap and with shading turned on - if all triangles have the same orientation, you will get a uniform surface; if not, the clockwise-oriented triangles will be darker than the others.
Although not required on sheet 4, please make sure for future tasks that your refinement routine is orientation-preserving and that your initial mesh is oriented. This should just require a simple modification. If you don't know how to achieve this, please ask your fellow students or contact me. A short introduction on orientations can be found in John M. Lee's "Introduction to Smooth Manifolds", Chapter 15.
Kind regards,
Ruben Gutendorf