A Balancing Domain Decomposition by Constraints Preconditioner for a $C^0$ Interior Penalty Method
Abstract
We develop a nonoverlapping domain decomposition preconditioner for the $C^0$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- 10.48550/arXiv.1811.06941
- arXiv:
- arXiv:1811.06941
- Bibcode:
- 2018arXiv181106941B
- Keywords:
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- Mathematics - Numerical Analysis;
- 65N30;
- 65N55
- E-Print:
- 8 pages, 2 figures, the 25th International Domain Decomposition Conference