The International Conference for High Performance Computing, Networking, Storage and Analysis
Performance of Block Jacobi-Davidson Eigensolvers.
Authors: Melven Roehrig-Zoellner (German Aerospace Center), Jonas Thies (German Aerospace Center), Moritz Kreutzer (Erlangen Regional Computing Center), Andreas Alvermann (University of Greifswald), Andreas Pieper (University of Greifswald), Achim Basermann (German Aerospace Center), Georg Hager (Erlangen Regional Computing Center), Gerhard Wellein (Erlangen Regional Computing Center), Holger Fehske (University of Greifswald)
Abstract: Jacobi-Davidson methods can efficiently compute a few eigenpairs of a large sparse matrix.
Block variants of Jacobi-Davidson are known to be more robust than the standard algorithm, but they are usually avoided as the total number of floating point operations increases.
We present the implementation of a block Jacobi-Davidson solver and show by detailed performance engineering and numerical experiments that the increase in operations is typically more than compensated by performance gains on modern architectures, giving a method that is both more efficient and robust than its single vector counterpart.