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Foundations of Computational Mathematics

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19-04-2023

Nodal Auxiliary Space Preconditioning for the Surface de Rham Complex

Author: Yuwen Li

Published in: Foundations of Computational Mathematics | Issue 3/2024

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Abstract

This work develops optimal preconditioners for the discrete H(curl) and H(div) problems on two-dimensional surfaces by nodal auxiliary space preconditioning (Hiptmair and Xu in SIAM J Numer Anal 45:2483–2509, 2007). In particular, on unstructured triangulated surfaces, we develop fast and user-friendly preconditioners for the edge and face element discretizations of curl–curl and grad–div problems based on inverting several discrete surface Laplacians. The proposed preconditioners lead to efficient iterative methods for computing harmonic tangential vector fields on discrete surfaces. Numerical experiments on two- and three-dimensional hypersurfaces are presented to test the performance of those surface preconditioners.

previous article Optimal Polynomial Meshes Exist on any Multivariate Convex Domain

next article A New Approach to Handle Curved Meshes in the Hybrid High-Order Method

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Title: Nodal Auxiliary Space Preconditioning for the Surface de Rham Complex
Author: Yuwen Li
Publication date: 19-04-2023
Publisher: Springer US
Published in: Foundations of Computational Mathematics / Issue 3/2024
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI: https://doi.org/10.1007/s10208-023-09611-0

A New Approach to Handle Curved Meshes in the Hybrid High-Order Method

Open Access

Optimal Polynomial Meshes Exist on any Multivariate Convex Domain

On the Computation of Geometric Features of Spectra of Linear Operators on Hilbert Spaces

Open Access

Subexponential-Time Algorithms for Sparse PCA

Correction to: Conormal Spaces and Whitney Stratifications

Open Access
Correction

Mathematics of 2-Dimensional Lattices

Open Access

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Nodal Auxiliary Space Preconditioning for the Surface de Rham Complex

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A New Approach to Handle Curved Meshes in the Hybrid High-Order Method

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Springer Professional "Wirtschaft+Technik"

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Correction to: Conormal Spaces and Whitney Stratifications

Mathematics of 2-Dimensional Lattices