  Nonlocal models allow for the description of phenomena which cannot be
captured by classical partial differential equations. The availability of
efficient solvers is one of the main concerns for the use of nonlocal models in
real world engineering applications. We present a domain decomposition solver
that is inspired by substructuring methods for classical local equations. In
numerical experiments involving finite element discretizations of scalar and
vectorial nonlocal equations of integrable and fractional type, we observe
improvements in solution time of up to 14.6x compared to commonly used solver
strategies.
