Solving discrete constrained problems on de Rham complex

2021/07/14 by Zhongjie Lu, Lu, Zhongjie
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2107.06695

openalex publication_date 2021/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main difficulty in solving the discrete constrained problem is its poor and even ill condition. In this paper, we transform the discrete constrained problems on de Rham complex to Laplace-like problems. This transformation not only make the constrained problems solvable, but also make it easy to use the existing iterative methods and preconditioning techniques to solving large-scale discrete constrained problems.

Citations

• Mixed finite elements in ?3
• Auxiliary iterative schemes for the discrete operators on de Rham complex

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