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Article

Čertíková, Marta ; Burda, Pavel ; Šístek, Jakub
Numerical comparison of different choices of interface weights in the BDDC method. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 55-61
MSC: 35J05, 65F08, 65F10, 65F35, 65N55 | MR 3204400 | Zbl 1313.65318
Keywords:
domain decomposition; interface weights; scaling; averaging; preconditioner; conjugate gradient methods; Poisson equation
Summary:
Balancing Domain Decomposition by Constraints (BDDC) belongs to the class of primal substructuring Domain Decomposition (DD) methods. DD methods are iterative methods successfully used in engineering to parallelize solution of large linear systems arising from discretization of second order elliptic problems. Substructuring DD methods represent an important class of DD methods. Their main idea is to divide the underlying domain into nonoverlapping subdomains and solve many relatively small, local problems on subdomains instead of one large problem on the whole domain. In primal methods, it has to be specified how to distribute interface residuals among subdomains and how to obtain global, interface values of solution from local values on adjacent subdomains. Usually a weighted average is used with some simple choice of weights. In our paper we present numerical comparison of three different choices of interface weights on test problem of 2D Poisson equation, with and without jumps in coefficients.
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