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Recent work on octree-based finite-element systems has developed a multigridsolver for Poisson equations on meshes. While the idea of defining a regularlyindexed function space has been successfully used in a number of applications,it has also been noted that the richness of the function space is limitedbecause the function values can be coupled across locally disconnected regions.In this work, we show how to enrich the function space by introducing functionsthat resolve the coupling while still preserving the nesting hierarchy thatsupports multigrid. A spectral analysis reveals the superior quality of theresulting Laplace-Beltrami operator and applications to surface flowdemonstrate that our new solver more efficiently converges to the correctsolution.

A Connectivity-Aware Multi-level Finite-Element System for Solving Laplace-Beltrami Equations