Split Grid and Block Lanczos Algorithm for Efficient Eigenpair Generation

The increasing imbalance between the computing capabilities of individual nodes and the internode bandwidth makes it highly desirable for any Lattice QCD algorithm to minimize the amount of internode communication. One of the relatively new methods for this is the Split Grid' or Split Domain’ method, where data is rearranged within the running of a single binary, so that the routines which requires significant off-node communications such as Dirac operators are run on multiple smaller partitions in parallel with a better surface to volume ratio, while other routines are run in one partition. While it is relatively straightforward to utilize Split Grid method for inverters, the typical Lanczos algorithm which has one starting vector does not render itself naturally to Split Grid method. In this report we investigate the Block Lanczos algorithm(BL), which allows multiple starting vectors to be processed in parallel. It is shown that for a moderate number of starting vectors, BL achieves convergence comparable to similarly tuned Implicitly Restarted Lanczos algorithm (IRL) on 2+1-flavor physical DWF/M"obius ensemble.