lkskstlr/map584

Ecole Polytechnique: MAP584 Implementation of Finite Element Methods

map584's Issues

Project from one mesh to another

It will be crucial to have the ability to project the solution from one mesh to another. This is a solved issue, see e.g. this cpp library.

However, it would be cool to implement part of it myself. The steps would/could be:

• Modify the function fe_space to support supplying an array of points x_int s.t. all operators U, DUX and DUY map from the degrees of freedom to the points in x_int. This will need a subroutine to determine which triangle an arbitrary point is in, e.g. from scipy.
• Write a routine that takes two meshes mesh1 and mesh2 and returns a mesh mesh3 s.t. all points from the input meshes and all intersections of edges are contained. Maybe much of the work can be done by triangle.
• Given two finite element functions in two meshes mesh1 and mesh2 first find the mesh from above and then get all integration points in it (high enough order, e.g. 4 for P2). Get the operators for the two meshes, construct the linear form and solve.

Memory continuousness

The instructions for the code including interfaces were written by Matlab programmers which often think in column vectors. Check for the critical code path if sometimes numpys 'F_CONTINUOUS' is superior to 'C_CONTINUOUS'.

Wrong boundary condition

In 9a64251 I forgot to leave the upper boundary without Dirichlet condition.