In Schwarz-like domain decomposition methods, a domain
is broken into two or more subdomains and
Dirichlet, Neumann, Robin or pseudo-differential problems
are iteratively solved on each subdomain. For certain
problems, it is well-known that the Dirichlet-Neumann
iteration for two subdomains will converge in two steps. Let
be an open domain and
a domain decomposition of
such that each pair of subdomains shares an
interface (for instance,
and
and
,
).
We will show a new Schwarz-like domain decomposition
method that converges in two iterations in this situation.