Fast auxiliary space preconditioners on surfaces

2020/11/27 by Li, Yuwen
#65F08 #65N30 #65N55 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2011.13502

Abstract

This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning (FASP), we develop efficient and user-friendly multilevel preconditioners for the Laplace--Beltrami type equation discretized by Lagrange, nonconforming linear, and discontinuous Galerkin elements. The analysis applies to semi-definite problems on a closed surface. Numerical experiments on 2d surfaces and 3d hypersurfaces are presented to illustrate the efficiency of the proposed preconditioners.

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