Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 321, Issue -, Pages 90-107Publisher
ELSEVIER
DOI: 10.1016/j.cam.2017.02.018
Keywords
Domain decomposition; Preconditioner; Bank-Hoist paradigm; Two-grid discretisations; Parallel adaptivity
Categories
Funding
- Numerical Algorithms and Intelligent Software Centre - UK EPSRC [EP/G036136]
- Scottish Funding Council
- Vietnam National Foundation for Science and Technology Development (NAFOSTED) [101.99-2017.13]
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A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenvalues of the preconditioned system. These eigenvalues can be bounded independently of the mesh sizes and the number of subdomains, which proves the proposed preconditioner is optimal. Numerical results are provided to support the theoretical findings. (C) 2017 Elsevier B.V. All rights reserved.
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