Balancing domain decomposition by constraints associated with subobjects
Abstract
A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number of the preconditioner is bounded by $C \big(1+\log (L/h)\big)^2$, where $C$ is a constant, and $h$ and $L$ are the characteristic sizes of the mesh and the subobjects, respectively. As $L$ can be chosen almost freely, the condition number can theoretically be as small as $O(1)$. We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.07289
- arXiv:
- arXiv:2001.07289
- Bibcode:
- 2020arXiv200107289B
- Keywords:
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- Mathematics - Numerical Analysis
- E-Print:
- Applied Mathematics Letters 87 (2019) 93-100