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