Adaptive BDDC in Three Dimensions

Abstract

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of variables. The effectiveness of the method is illustrated on several engineering problems.

arXiv comment28 pages, 9 figures, 9 tables

References in corpus (4)

• Multispace and Multilevel BDDC
• BDDC and FETI-DP under Minimalist Assumptions
• On the Equivalence of Primal and Dual Substructuring Preconditioners
• BDDC by a frontal solver and the stress computation in a hip joint replacement

Cited by in corpus (9)

• BDDC and FETI-DP algorithms with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients
• Adaptive-Multilevel BDDC and its parallel implementation
• Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods
• Application of the parallel BDDC preconditioner to the Stokes flow
• Face-based Selection of Corners in 3D Substructuring
• On Adaptive-Multilevel BDDC
• BDDC for Mixed-Hybrid Formulation of Flow in Porous Media with Combined Mesh Dimensions
• A two-level overlapping Schwarz method with energy-minimizing multiscale coarse basis functions
• Speeding up an unsteady flow simulation by adaptive BDDC and Krylov subspace recycling