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**Numerical comparison of different choices of interface weights in the BDDC method.**
*(English)*
Zbl 1313.65318

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 2–5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-60-8/pbk). 55-61 (2012).

The authors compare three choices of interface weights in the context of nonoverlapping domain decomposition methods. The performance of these choices is tested for balancing domain decomposition based on constraints (BDDC) applied as a preconditioner within the Richardson and preconditioned conjugate gradient methods. The model problem is the Poisson equation in 2D without and with a jump in the coefficient along the interface between two subdomains. The study is limited to a rather small problem containing only 35 bilinear elements and 4 subdomains. In addition, the coefficients are constant on each subdomain in the example. The results reveal the sufficient performance of the simplest choice, the arithmetic average, for homogeneous problems. This method, however, becomes inefficient if jumps in coefficients are present, in which case the scaling by diagonal stiffness and authors’ own proposition work well and lead to a comparable number of iterations.

For the entire collection see [Zbl 1277.00031].

For the entire collection see [Zbl 1277.00031].

Reviewer: Bedřich Sousedík (College Park)

### MSC:

65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |

65F08 | Preconditioners for iterative methods |

65F10 | Iterative numerical methods for linear systems |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |

65F35 | Numerical computation of matrix norms, conditioning, scaling |

### Keywords:

domain decomposition; interface weights; scaling; averaging; preconditioner; conjugate gradient methods; Poisson equation
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\textit{M. Čertíková} et al., in: Proceedings of the international conference `Applications of mathematics', Prague, Czech Republic, May 2--5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 55--61 (2012; Zbl 1313.65318)

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