Beyond AMLS: Domain decomposition with rational filtering
For researchers solving large-scale eigenvalue problems, this method offers a new algebraic domain decomposition approach that reduces communication and avoids eigenvalue count estimation.
This paper introduces a rational filtering domain decomposition method for solving large sparse symmetric generalized eigenvalue problems, which decomposes the problem into interface and interior subproblems. Numerical experiments show it is competitive with rational filtering Krylov methods on distributed memory architectures.
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.