Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 40, Issue 1, Pages 764-799Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/dry032
Keywords
BPX preconditioner; isogeometric analysis; analysis-suitable T-splines
Categories
Funding
- Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Science, ICT & Future Planning [2015R1A1A1A05001109]
- European Research Council [616563]
- FP7 ERC [694515]
- European Union [680448]
- H2020 Societal Challenges Programme [680448] Funding Source: H2020 Societal Challenges Programme
- European Research Council (ERC) [616563] Funding Source: European Research Council (ERC)
- National Research Foundation of Korea [2015R1A1A1A05001109] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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We propose and analyse optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern & Peterseim (2015, Analysis-suitable adaptive T-mesh refinement with linear complexity. Comput. Aided Geom. Design, 34, 50-66) we can guarantee that the obtained T-meshes have a multilevel structure and that the associated T-splines are analysis suitable, for which we can define a dual basis and a stable projector. Taking advantage of the multilevel structure we develop two Bramble-Pasciak-Xu (BPX) preconditioners: the first on the basis of local smoothing only for the functions affected by a newly added edge by bisection and the second smoothing for all the functions affected after adding all the edges of the same level. We prove that both methods have optimal complexity and present several numerical experiments to confirm our theoretical results and also to compare the practical performance of the proposed preconditioners.
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