A Balancing Domain Decomposition by Constraints Preconditioner for a C⁰ Interior Penalty Method

2018/11/16 by Susanne C. Brenner, Eun‐Hee Park, Brenner, Susanne C. +5 · 1 citation
Computer Science · Engineering · #65N30 #65N55 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1811.06941

openalex publication_date 2018/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We develop a nonoverlapping domain decomposition preconditioner for the C⁰ interior penalty method, a discontinuous Galerkin method, for the biharmonic problem. The preconditioner is based on balancing domain decomposition by constraints (BDDC). We prove that the condition number of the preconditioned system is bounded by C (1+ln (H/h))², where h is the mesh size of the triangulation, H is the typical diameter of subdomains, and the positive constant C is independent of h and H. Numerical experiments are also represented to corroborate the theoretical result.

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