In numerical analysis, BDDC (balancing domain decomposition by constraints) is a domain decomposition method for solving large symmetric, positive definite systems of linear equations that arise from the finite element method.
The local problems on different subdomains are completely independent of each other, so the method is suitable for parallel computing.
BDDC was introduced by different authors and different approaches at about the same time, i.e., by Cros,[1] Dohrmann,[2] and Fragakis and Papadrakakis,[3] as a primal alternative to the FETI-DP domain decomposition method by Farhat et al.[4][5] See [6] for a proof that these are all actually the same method as BDDC.
The elasticity problem is to determine the deformation of a structure subject to prescribed displacements and forces applied to it.
After applying the finite element method, we obtain a system of linear algebraic equations, where the unknowns are the displacements at the nodes of the elements and the right-hand side comes from the forces (and from nonzero prescribed displacements on the boundary, but, for simplicity, assume that these are zero).
In a practical implementation, the right-hand-side and the initial approximation for the iterations are preprocessed so that all forces inside the subdomains are zero.
Then the forces inside the subdomains stay zero during the conjugate gradients iterations, and so the first interior correction in each application of BDDC can be omitted.