I am trying to use the finite element method to solve the Laplace-Beltrami eigenvalue problem on a surface (i.e., a 2D dimensional manifold) embedded in 3-dimensional space, for example, the boundary of a sphere or torus. I managed to generate the triangular mesh (its points and triangles) using the Pyvista library.
points = [[-2.5819006 -6.5754533 -2.0017405]
[-2.6988158 -6.5754533 -1.9960535]
[-2.5819006 -6.604572 -1.9960535]
...
[ 1.4294114 7.86527 1.7230791]
[ 2.2316737 7.86527 1.6120211]
[ 3.0339363 7.86527 1.388944 ]]
cells = [[ 0 1 2]
[ 2 3 0]
[ 4 5 6]
...
[ 925 1144 924]
[1145 1144 925]
[ 909 1145 925]]
Now I am looking for a simple finite element solver.
Usually, I use the scikit-fem library which works well in situations with flat 2-dimensional triangular meshes or tetrahedral meshes in 3D shapes. However, it can not handle triangular meshes of 2-dimensional surfaces in 3-dimensional space. Which package can easily solve the Laplace-Beltrami eigenvalue problem for such meshes?