Theoretically supported scalable BETI method for variational inequalities

Summary The Boundary Element Tearing and Interconnecting (BETI) methods were recently introduced as boundary element counterparts of the well established Finite Element Tearing and Interconnecting (FETI) methods. Here we combine the BETI method preconditioned by the projector to the “natural coarse...

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Bibliographic Details
Published in:Computing 2008-04, Vol.82 (1), p.53-75
Main Authors: Bouchala, Jiři, Dostál, Z., Sadowská, M.
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied mathematics
Applied sciences
Artificial Intelligence
Calculus of variations and optimal control
Computer Appl. in Administrative Data Processing
Computer Communication Networks
Computer Science
Computer science
control theory
systems
Decomposition
Exact sciences and technology
Information Systems Applications (incl.Internet)
Mathematical analysis
Mathematics
Methods
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Optimization
Partial differential equations
Quadratic programming
Sciences and techniques of general use
Software Engineering
Studies
Theoretical computing
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Summary:Summary The Boundary Element Tearing and Interconnecting (BETI) methods were recently introduced as boundary element counterparts of the well established Finite Element Tearing and Interconnecting (FETI) methods. Here we combine the BETI method preconditioned by the projector to the “natural coarse grid” with recently proposed optimal algorithms for the solution of bound and equality constrained quadratic programming problems in order to develop a theoretically supported scalable solver for elliptic multidomain boundary variational inequalities such as those describing the equilibrium of a system of bodies in mutual contact. The key observation is that the “natural coarse grid” defines a subspace that contains the solution, so that the preconditioning affects also the non-linear steps. The results are validated by numerical experiments.
ISSN:0010-485X
1436-5057
DOI:10.1007/s00607-008-0257-3