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

Čertíková, Marta; Burda, Pavel; Šístek, Jakub

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].

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