Abstract

We present preliminary results of an ongoing project to develop codes of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for symmetric eigenvalue problems for Hypre and PETSc software packages. Hypre and PETSc packages provide high quality multigrid and domain decomposition preconditioning on parallel clusters with distributed or shared memory architecture. The LOBPCG method, suggested and developed by Andrew Knyazev [1] in the past decade, recently attracts an increasing attention as a potential alternative to the shift-and-invert Lanczos and preconditioned Davidson methods due to its simplicity robustness and fast convergence. Several MATLAB, C, C++ and FORTRAN implementations of the LOBPCG are developed by different groups, e. g., for such applications areas as structured mechanics and electronic structure calculations. However, the only publicly available at present LOBPCG implementation remains our implementation for Hypre, which is already included in Hypre 1.8.2 release. We describe the current state of the LOBPCG software for Hypre and PETSc, developed by our group and demonstrate initial scalability results.

[1] A.V. Knyazev, "Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method."
SIAM Journal on Scientific Computing 23 (2001), no. 2, pp. 517-541.