  This paper proposes a rational filtering domain decomposition technique for
the solution of large and sparse symmetric generalized eigenvalue problems. The
proposed technique is purely algebraic and decomposes the eigenvalue problem
associated with each subdomain into two disjoint subproblems. The first
subproblem is associated with the interface variables and accounts for the
interaction among neighboring subdomains. To compute the solution of the
original eigenvalue problem at the interface variables we leverage ideas from
contour integral eigenvalue solvers. The second subproblem is associated with
the interior variables in each subdomain and can be solved in parallel among
the different subdomains using real arithmetic only. Compared to rational
filtering projection methods applied to the original matrix pencil, the
proposed technique integrates only a part of the matrix resolvent while it
applies any orthogonalization necessary to vectors whose length is equal to the
number of interface variables. In addition, no estimation of the number of
eigenvalues lying inside the interval of interest is needed. Numerical
experiments performed in distributed memory architectures illustrate the
competitiveness of the proposed technique against rational filtering Krylov
approaches.
