Authors: MaCLARK R. DOHRMANN AND OLOF B. WIDLUND

Title: AN ITERATIVE SUBSTRUCTURING ALGORITHM FOR TWO-DIMENSIONAL PROBLEMS IN H(CURL)

Abstract:
A domain decomposition algorithm, similar to classical iterative substructuring algorithms,
is presented for two-dimensional problems in the space H0(curl). It is defined in terms 
of a coarse space and local subspaces associated with individual edges of the subdomains into which
the domain of the problem has been subdivided. The algorithm differs from others in three basic
respects. First, it can be implemented in an algebraic manner that does not require access to individual
subdomain matrices or a coarse discretization of the domain; this is in contrast to algorithms
of the BDDC, FETI–DP, and classical two–level overlapping Schwarz families. Second, favorable
condition number bounds can be established over a broader range of subdomain material properties
than in previous studies. Third, we are able to develop theory for quite irregular subdomains and
bounds for the condition number of our preconditioned conjugate gradient algorithm, which depend
only on a few geometric parameters.
The coarse space for the algorithm is based on simple energy minimization concepts, and its
dimension equals the number of subdomain edges. Numerical results are presented which confirm
the theory and demonstrate the usefulness of the algorithm for a variety of mesh decompositions and
distributions of material properties.