Title: A BDDC algorithm for problems with mortar discretization

(NYU-CS-TR873)

Authors:  Hyea Hyun Kim, Maksymilian Dryja, and Olof B. Widlund

Abstract:

A BDDC (balancing domain decomposition by constraints) algorithm
is developed for elliptic problems with mortar discretizations for
geometrically non-conforming partitions in both two and three
spatial dimensions. The coarse component of the preconditioner is
defined in terms of one mortar constraint for each edge/face which
is an intersection of the boundaries of a pair of subdomains. A
condition number bound of the form $C \max_i \left\{ (1+\text{log} (H_i/h_i) )3 \right\}$ is established. In geometrically
conforming cases, the bound can be improved to $C \max_i \left\{ (1+\text{log} (H_i/h_i) )2 \right\}$. This estimate is also valid
in the geometrically nonconforming case under an additional
assumption on the ratio of mesh sizes and jumps of the
coefficients. This BDDC preconditioner is also shown to be closely
related to the Neumann-Dirichlet preconditioner for the FETI--DP
algorithms of \cite{K-04-3d,KL-02} and it is shown that the
eigenvalues of the BDDC and FETI--DP methods are the same except
possibly for an eigenvalue equal to 1.