Premium
Automatic spectral coarse spaces for robust finite element tearing and interconnecting and balanced domain decomposition algorithms
Author(s) -
Spillane N.,
Rixen D.J.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4534
Subject(s) - preconditioner , domain decomposition methods , finite element method , tearing , convergence (economics) , mathematics , condition number , eigenvalues and eigenvectors , domain (mathematical analysis) , scalability , matrix decomposition , element (criminal law) , eigendecomposition of a matrix , algorithm , decomposition , mathematical analysis , mathematical optimization , computer science , structural engineering , iterative method , engineering , physics , mechanical engineering , database , economic growth , ecology , biology , quantum mechanics , political science , economics , law
SUMMARY We introduce spectral coarse spaces for the balanced domain decomposition and the finite element tearing and interconnecting methods. These coarse spaces are specifically designed for the two‐level methods to be scalable and robust with respect to the coefficients in the equation and the choice of the decomposition. We achieve this by solving generalized eigenvalue problems on the interfaces between subdomains to identify the modes that slow down convergence. Theoretical bounds for the condition numbers of the preconditioned operators, which depend only on a chosen threshold, and the maximal number of neighbors of a subdomain are presented and proved. For the finite element tearing and interconnecting method, there are two versions of the two‐level method: one based on the full Dirichlet preconditioner and the other on the, cheaper, lumped preconditioner. Some numerical tests confirm these results. Copyright © 2013 John Wiley & Sons, Ltd.