Fast auxiliary space preconditioners on surfaces

11/27/2020
by   Yuwen Li, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/16/2021

Nodal auxiliary space preconditioning for the surface de Rham complex

This work develops optimal preconditioners for the discrete H(curl) and ...
research
12/31/2020

Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud

A generic geometric error analysis framework for numerical solution of P...
research
08/20/2021

On the numerical solution of the Laplace-Beltrami problem on piecewise-smooth surfaces

The Laplace-Beltrami problem on closed surfaces embedded in three dimens...
research
05/05/2021

Auxiliary iterative schemes for the discrete operators on de Rham complex

The main difficulty in solving the discrete source or eigenvalue problem...
research
05/31/2022

Local discontinuous Galerkin method for the Backward Feynman-Kac Equation

Anomalous diffusions are ubiquitous in nature, whose functional distribu...
research
01/13/2021

Approximation of the spectral fractional powers of the Laplace-Beltrami Operator

We consider numerical approximation of spectral fractional Laplace-Beltr...
research
05/05/2018

Polar Wavelets in Space

Recent work introduced a unified framework for steerable and directional...

Please sign up or login with your details

Forgot password? Click here to reset