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We describe our software package Block Locally Optimal PreconditionedEigenvalue Xolvers (BLOPEX) publicly released recently. BLOPEX is available asa stand-alone serial library, as an external package to PETSc (``Portable,Extensible Toolkit for Scientific Computation'', a general purpose suite oftools for the scalable solution of partial differential equations and relatedproblems developed by Argonne National Laboratory), and is also built into {\ithypre} (``High Performance Preconditioners'', scalable linear solvers packagedeveloped by Lawrence Livermore National Laboratory). The present BLOPEXrelease includes only one solver--the Locally Optimal Block PreconditionedConjugate Gradient (LOBPCG) method for symmetric eigenvalue problems. {\ithypre} provides users with advanced high-quality parallel preconditioners forlinear systems, in particular, with domain decomposition and multigridpreconditioners. With BLOPEX, the same preconditioners can now be efficientlyused for symmetric eigenvalue problems. PETSc facilitates the integration ofindependently developed application modules with strict attention to componentinteroperability, and makes BLOPEX extremely easy to compile and use withpreconditioners that are available via PETSc. We present the LOBPCG algorithmin BLOPEX for {\it hypre} and PETSc. We demonstrate numerically the scalabilityof BLOPEX by testing it on a number of distributed and shared memory parallelsystems, including a Beowulf system, SUN Fire 880, an AMD dual-core Opteronworkstation, and IBM BlueGene/L supercomputer, using PETSc domain decompositionand {\it hypre} multigrid preconditioning. We test BLOPEX on a model problem,the standard 7-point finite-difference approximation of the 3-D Laplacian, withthe problem size in the range $10^5-10^8$.

Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc