A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients
SIAM Journal on Numerical Analysis
A Preconditioner for Substructuring Based on Constrained Energy Minimization
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Multispace and multilevel BDDC
Computing
An algebraic theory for primal and dual substructuring methods by constraints
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
BDDC by a frontal solver and the stress computation in a hip joint replacement
Mathematics and Computers in Simulation
Original Article: Adaptive BDDC in three dimensions
Mathematics and Computers in Simulation
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In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a 'minimal' set of coarse nodes (sometimes called corners) which assures invertibility of local subdomain problems and also of the global coarse problem. This basic set is typically enhanced by enforcing continuity of functions at some generalized degrees of freedom, such as average values on edges or faces of subdomains. We revisit existing algorithms for selection of corners. The main contribution of this paper consists of proposing a new heuristic algorithm for this purpose. Considering faces as the basic building blocks of the interface, inherent parallelism, and better robustness with respect to disconnected subdomains are among features of the new technique. The advantages of the presented algorithm in comparison to some earlier approaches are demonstrated on three engineering problems of structural analysis solved by the BDDC method.