Performance comparison of parallel eigensolvers based on a contour integral method and a Lanczos method

We study the performance of a parallel nonlinear eigensolver SSEig which is based on a contour integral method. We focus on symmetric generalized eigenvalue problems (GEPs) of computing interior eigenvalues. We chose to focus on GEPs because we can then compare the performance of SSEig with that of a publicly-available software package TRLan, which is based on a thick restart Lanczos method. To solve this type of problems, SSEig requires the solution of independent linear systems with different shifts, while TRLan solves a sequence of linear systems with a single shift. Therefore, while SSEig typically has a computational cost greater than that of TRLan, it also has greater parallel scalability. To compare the performance of these two solvers, in this paper, we develop performance models and present numerical results of solving large-scale eigenvalue problems arising from simulations of modeling accelerator cavities. In particular, we identify the crossover point, where SSEig becomes faster than TRLan. The parallel performance of SSEig solving nonlinear eigenvalue problems is also studied.