Software concepts and numerical algorithms for a scalable adaptive parallel finite element method

An efficient implementation of an adaptive finite element method on distributed memory systems requires an efficient linear solver. Most solver methods, which show scalability to a large number of processors make use of some geometric information of the mesh. This information has to be provided to t...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 41; no. 6; pp. 1145 - 1177
Main Authors Witkowski, T., Ling, S., Praetorius, S., Voigt, A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2015
Subjects
Algorithms
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Data structures
Distributed memory
Finite element method
Mathematical analysis
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Numerical analysis
Processors
Solvers
Visualization
Software concepts
65M60
65Y20
High performance computing
65Y05
Adaptive finite elements
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Summary:An efficient implementation of an adaptive finite element method on distributed memory systems requires an efficient linear solver. Most solver methods, which show scalability to a large number of processors make use of some geometric information of the mesh. This information has to be provided to the solver in an efficient and solver specific way. We introduce data structures and numerical algorithms which fulfill this task and allow in addition for an user-friendly implementation of a large class of linear solvers. The concepts and algorithms are demonstrated for global matrix solvers and domain decomposition methods for various problems in fluid dynamics, continuum mechanics and materials science. Weak and strong scaling is shown for up to 16.384 processors.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-015-9405-4