Parallele Teilraumverfahren zur Bestimmung von Eigenwerten im Innern des Spektrums

Eigenvalue problems in which just a few eigenvalues and -vectors of a large and sparre matrix have to be determined are typically solved by subspace methods. This requires the distinction between the computation of extreme eigenvalues and the computation of eigenvalues within the neighbourhood of a prescribed shift in the interior of the spectrum. Whereas for extreme eigenvalues a large number of fast converging methods can be found the computation of interior eigenvalues proves to be significantly more difficult and only a few suitable methods exist. In this thesis a new method for the computation of interior eigenvalues is developed consisting of a Jacobi-Davidson method and a technique based on the idea of residual minimization. For the resulting method an implementation on a massively-parallel computing system is designed which is not only characterized by minimal communication costs but also allows a clever combination of the method with residual minimization and the harmonie Jacobi-Davidson method