interpolate Morley

The problem is to interpolate a function defined on Morley elements at a specified (x, y) point which isn’t necessarily a node; e.g. the deflection at the centre of the Kirchhoff plate in ex02, or the value of the stream-function at the centre of the circular-cylindrical cavity in ex18.

Attempting MeshTri.interpolator with the MeshTri returned by refinterp fails #59; the mesh is invalid, having duplicate points.

I think interpolation involves two steps:

1. Find the element (if any) that contains the point.
2. Evaluate the function based on the local basis functions of that element and the elemental degrees of freedom.

and I suspect that in general the first is the harder.

Thus far, this operation is only implemented in scikit-fem as MeshTri.interpolator (P1) and MeshTri.const_interpolator (P0) and makes use of :

• matplotlib.tri.Triangulation,
• matplotlib.tri.LinearTriInterpolator
• matplotlib.tri.Triangulation.get_trifinder

Perhaps the TriFinder might be factored out of those so that it could also be used for other elements defined on linear simplicial meshes; e.g., besides Morley, also affine P2. Looking ahead, with MeshQuad._splitquads, perhaps quadrilateral meshes too.

[kinnala]

cc99ad97b335c1698816c19b83fa46dc1683b6f0 should fix interpolating ElementH2 bases. Support for multiple elements was missing in MappingAffine.F.

[kinnala]

When you read the source code in Github and mouse over the line number, three dots apper next to it. Pressing that gives you a URL.