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

Community Petascale Project for Accelerator Science and Simulation (ComPASS). <https://compass.fnal.gov>. Amestoy, 2001, Analysis and comparison of two general sparse solvers for distributed memory computers, ACM Trans. Math. Software, 388, 10.1145/504210.504212 Asakura, 2009, A numerical method for nonlinear eigenvalue problems using contour integrals, JSIAM Lett., 1, 52, 10.14495/jsiaml.1.52 M. Baertschy, X.S. Li, Solution of a three-body poblem in quantum mechanics, in: Proceedings of SC2001: High Performance Networking and Computing Conference, Denver, Colorado, November 10–16, 2001. Futamura, 2010, Parallel stochastic estimation method for eigenvalue distribution, JSIAM Lett., 2, 127, 10.14495/jsiaml.2.127 Grimes, 1994, A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems, SIAM J. Matrix Anal. Appl., 15, 228, 10.1137/S0895479888151111 Ikegami, 2010, Contoure integral eigensolver for non-Hermitian systems: a Rayleigh–Ritz-type approach, Taiwanese J. Math., 14, 825, 10.11650/twjm/1500405869 Ikegami, 2010, A filter diagonalization for generalized eigenvalue problems based on the Sakurai–Sugiura projection method, J. Comput. Appl. Math., 233, 1927, 10.1016/j.cam.2009.09.029 T. Ikegami, H. Tadano, H. Umeda, T. Sakurai, Hierachical parallel algorithm to solve large generalized eigenvalue problems, in: The Proceedings of the International Conference on High Performance Computing and Simulation (HPCS), 2010, pp. 107–114. L.-Q. Lee, Z. Li, C.-K. Ng, K. Ko, Omega3P: a parallel finite-element eigenmode analysis code for accelerator cavities, Technical Report SLAC-PUB-13529, Stanford Linear Accelerator Center, 2009. Li, 2003, SuperLU_DIST: a scalable distributed-memory sparse direct solver for unsymmetric linear systems, ACM Trans. Math. Software, 29, 110, 10.1145/779359.779361 B.-S. Liao, Z. Bai, L.-Q. Lee, K. Ko, Solving large scale nonlinear eigenvalue problem in next-generation accelerator design, Technical Report SLAC-PUB-12137, Stanford Linear Accelerator Center, 2006. Parlett, 1998 Saad, 1993 Sakurai, 2009, Error analysis for a matrix pencil of Hankel matrices with perturbed complex moments, JSIAM Lett., 1, 76, 10.14495/jsiaml.1.76 Sakurai, 2003, A projection method for generalized eigenvalue problems, J. Comput. Appl. Math., 159, 119, 10.1016/S0377-0427(03)00565-X Sakurai, 2007, CIRR: a Rayleigh–Ritz type method with contour integral for generalized eigenvalue problems, Hokkaido Math. J., 36, 745, 10.14492/hokmj/1272848031 T. Sakurai, H. Tadano, T. Ikegami, I. Yamazaki, A comparative study of parallel generalized eigenvalue solvers with an application to accelerator cavity design, available from: <http://www.cs.tsukuba.ac.jp/∼sakurai/SIAM_PP10.pdf>, in: The Poster Session of the SIAM Parallel Processing for Scientific Computing (PP10), 2010. K. Senzaki, H. Tadano, T. Sakurai, Z. Bai, A method for estimating the distribution of eigenvalues using the AS methods, in: Proceedings of the International Conference of Recent Advances in Numerical Methods for Eigenvalue Problems, Taiwanese J. Math., vol. 14, 2010, pp. 839–853. K. Wu, H. Simon, Dynamic restarting schemes for eigenvalue problems, Technical Report LBNL-42982, Lawrence Berkeley National Laboratory, 1999. K. Wu, H. Simon, A parallel Lanczos method for symmetric generalized eigenvalue problems, Technical Report LBNL-41284, Lawrence Berkeley National Laboratory, 1999. Wu, 2000, Thick-restart Lanczos method for large symmetric eigenvalue problems, SIAM J. Math. Anal. Appl., 22, 602, 10.1137/S0895479898334605 Yamazaki, 2010, Adaptive projection subspace dimension for the thick-restart Lanczos method, ACM Trans. Math. Software, 37, 10.1145/1824801.1824805 I. Yamazaki, X. Li, E. Ng, Preconditioning schur complement systems of highly-indefinite linear systems for a parallel hybrid solver, in: The Proceedings of the International Conference on Preconditioning Techniques For Scientific and Industrial Applications, 2009. I. Yamazaki, K. Wu, H. Simon, nu-TRLan user guide, Technical Report LBNL-1288E, Lawrence Berkeley National Laboratory, 2008.