Balancing domain decomposition for problems with large jumps in coefficients
Mathematics of Computation
A Neumann--Neumann Domain Decomposition Algorithm for Solving Plate and Shell Problems
SIAM Journal on Numerical Analysis
A Scalable Substructuring Method by Lagrange Multipliers for Plate Bending Problems
SIAM Journal on Numerical Analysis
A Domain Decomposition Method with Lagrange Multipliers and Inexact Solvers for Linear Elasticity
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
Boundary element tearing and interconnecting methods in unbounded domains
Applied Numerical Mathematics
BDDC by a frontal solver and the stress computation in a hip joint replacement
Mathematics and Computers in Simulation
A FETI-DP Formulation for the Stokes Problem without Primal Pressure Components
SIAM Journal on Numerical Analysis
Robust BDDC Preconditioners for Reissner-Mindlin Plate Bending Problems and MITC Elements
SIAM Journal on Numerical Analysis
A FETI-DP Formulation for the Three-Dimensional Stokes Problem without Primal Pressure Unknowns
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
BDDC preconditioners for Naghdi shell problems and MITC9 elements
Computers and Structures
SIAM Journal on Scientific Computing
Mathematics and Computers in Simulation
Original article: Face-based selection of corners in 3D substructuring
Mathematics and Computers in Simulation
Original Article: Adaptive BDDC in three dimensions
Mathematics and Computers in Simulation
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Journal of Computational Physics
A BDDC algorithm for a class of staggered discontinuous Galerkin methods
Computers & Mathematics with Applications
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FETI and BDD are two widely used substructuring methods for the solution of large sparse systems of linear algebraic equations arising from discretization of elliptic boundary value problems. The two most advanced variants of these methods are the FETI-DP and the BDDC methods, whose formulation does not require any information beyond the algebraic system of equations in a substructure form. We formulate the FETI-DP and the BDDC methods in a common framework as methods based on general constraints between the substructures, and provide a simplified algebraic convergence theory. The basic implementation blocks including transfer operators are common to both methods. It is shown that commonly used properties of the transfer operators in fact determine the operators uniquely. Identical algebraic condition number bounds for both methods are given in terms of a single inequality, and, under natural additional assumptions, it is proved that the eigenvalues of the preconditioned problems are the same. The algebraic bounds imply the usual polylogarithmic bounds for finite elements, independent of coefficient jumps between substructures. Computational experiments confirm the theory.