# BDDC Deluxe Domain Decomposition

## Abstract

We will consider BDDC domain decomposition algorithms for finite element approximations of a variety of elliptic problems. The BDDC (Balancing Domain Decomposition by Constraints) algorithms were introduced by Dohrmann [5], following the introduction of FETI-DP by Farhat et al. [9]. These two families are closely related algorithmically and have a common theory. The design of a BDDC algorithm involves the choice of a set of *primal degrees of freedom* and the choice of an *averaging operator*, which restores the continuity of the approximate solution across the interface between the subdomains into which the domain of the given problem has been partitioned. We will also refer to these operators as *scalings*.

## Keywords

Domain Decomposition Isogeometric Analysis Primal Space Preconditioned Conjugate Gradient Method Nodal Finite Element## Notes

### Acknowledgement

The first author was supported in part by the National Science Foundation Grant DMS-1216564 and in part by the U.S. Department of Energy under contract DE-FE02-06ER25718. The second author is a member of the Computational Solid Mechanics and Structural Dynamics Department, Sandia National Laboratories, Albuquerque, New Mexico. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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