  This paper introduces a novel geometric multigrid solver for unstructured
curved surfaces. Multigrid methods are highly efficient iterative methods for
solving systems of linear equations. Despite the success in solving problems
defined on structured domains, generalizing multigrid to unstructured curved
domains remains a challenging problem. The critical missing ingredient is a
prolongation operator to transfer functions across different multigrid levels.
We propose a novel method for computing the prolongation for triangulated
surfaces based on intrinsic geometry, enabling an efficient geometric multigrid
solver for curved surfaces. Our surface multigrid solver achieves better
convergence than existing multigrid methods. Compared to direct solvers, our
solver is orders of magnitude faster. We evaluate our method on many geometry
processing applications and a wide variety of complex shapes with and without
boundaries. By simply replacing the direct solver, we upgrade existing
algorithms to interactive frame rates, and shift the computational bottleneck
away from solving linear systems.
