  The first domain decomposition methods for partial differential equations
were already developed in 1870 by H. A. Schwarz. Here we consider a nonlocal
Dirichlet problem with variable coefficients, where a nonlocal diffusion
operator is used. We find that domain decomposition methods like the so-called
Schwarz methods seem to be a natural way to solve these nonlocal problems. In
this work we show the convergence for nonlocal problems, where specific
symmetric kernels are employed, and present the implementation of the
multiplicative and additive Schwarz algorithms in the above mentioned nonlocal
setting.
