|
| |
|
|
Different approaches to interface weights in the BDDC method in 3D
Čertíková, M. ; Šístek, Jakub ; Burda, P.
In this paper, we discuss the choice of weights in averaging of local (subdomain) solutions on the interface for the BDDC method (Balancing Domain Decomposition by Constraints). We try to find relations among different choices of the interface weights and compare them numerically on model problems of the Poisson equation and linear elasticity in 3D. Problems with jumps in coefficients of material properties are considered and both regular and irregular interfaces between subdomains are tested.
|
|
|
On selection of interface weights in domain decomposition methods
Čertíková, M. ; Šístek, Jakub ; Burda, P.
Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included into the study. Two new approaches are studied along three standard choices. No approach is shown to be universally superior to others, and the resulting recommendation is that an actual method should be chosen based on properties of the problem.
|
|
|
Numerical comparison of different choices of interface weights in the BDDC method
Čertíková, M. ; Burda, P. ; Šístek, Jakub
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 solvemany 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.
|
|
| |
|
|
Approaches to parallel implementation of the BDDC method
Šístek, Jakub ; Burda, P. ; Čertíková, M. ; Novotný, J.
During past several years, we have implemented and tested various approaches to domain decomposition methods, especially the Balancing Domain Decomposition Method by Constraints (BDDC). The goal of this paper is to summarize our experience with parallel implementation of such algorithms and to suggest ways to an implementation of the BDDC method that would be efficient on very large number of cores of computers of near future.
|
|
|
On selections of constraints for the BDDC method
Čertíková, M. ; Šístek, Jakub ; Novotný, J. ; Burda, P.
The Balancing Domain Decomposition by Constraints (BDDC) method is an iterative substructuring domain decomposition method which uses a coarse space. The choice of coarse constraints on continuity has strong influence on convergence of the method. The goal of this paper is to compare the performance of several algorithms for selection of the coarse constraints applied to both test and industrial 3D linear elasticity problems and confront results obtained for typical test problems with results for industrial problems.
|
|
| |
|
| |
|
| |
host ::
RSS.