Computing eigenvalues of integral operators: a distributed memory computing approach

In this presentation we address the parallel implementation of the Multi-Power Defect-Correction method for the computation of eigenpairs of compact integral operators. The integral operator is discretized by a projection method on a subspace of moderate dimension and the eigenelements of its representing matrix are computed. These are then iteratively refined, by a defect correction type procedure accelerated by a few power iterations, to yield a better approximation to the spectral elements of the operator. The algorithm is rich in matrix-vector multiplications involving matrices whose construction is distributed among the available processors. The defect correction phase requires the solution of a distributed linear system of moderate dimension. Computational approaches of parallelization using state-of-the-art packages will be discussed, and numerical results on an astrophysics application, whose mathematical model involves a weakly singular integral operator, will be presented. Co-authors: Filomena Dias d'Almeida (Faculdade de Engenharia da Universidade do Porto) e José E. Roman (Instituto ITACA, Universidad Politécnica de Valencia, Spain)