Convergence of a Substructuring Method with Lagrange multipliers
Jan Mandel and Radek Tezaur
We analyze the convergence of a substructuring iterative method with Lagrange
multipliers, proposed recently by Farhat and Roux. The method decomposes
finite element discretization of an elliptic boundary value problem into
Neumann problems on the subdomains plus a coarse problem for the subdomain
nullspace components. For linear conforming elements and preconditioning by
the Dirichlet problems on the subdomains, we prove the asymptotic bound on the
condition number $C (1+\log (H/h))^\alpha$, $\alpha=2$ or $3$,where $h$ is the
characteristic element size, $H$ subdomain size, and $C$ is independent of the
number of subdomains.