Anasazi: A Block Eigensolvers Package

TrilinosRelease7.0Branch

Introduction

Anasazi is an extensible and interoperable framework for the numerical solution of large-scale eigenvalue algorithms implemented in templated ANSI C++. The motivation for this framework is to provide a generic interface to a collection of algorithms for solving large-scale eigenvalue problems. Anasazi is interoperable because both the matrix and vectors (defining the eigenspace) are considered to be opaque objects---only knowledge of the matrix and vectors via elementary operations is necessary. Hence the user has the flexibility to specify the data representation (existing data structures) for the matrix and vectors and so leverage any existing software investment. This flexibility is accomplished with the software interface Anasazi Operator/Vector abstract interface.

The Anasazi eigensolver framework describes eigensolver and eigensolver managers that allow for efficient, convenient and powerful computational ability.

Current interfaces available include Epetra and so any libraries that understand Epetra matrices and vectors (such as other packages in Trilinos) may also be used in conjunction with Anasazi.

Current Eigensolvers

The algorithms that are currently available are:

• Block Krylov-Schur method, a block extension of A Krylov-Schur Algorithm for Large Eigenproblems, G. W. Stewart, SIAM J. Matrix Anal. Appl., 23, pp. 601-614.
• Block Davidson method described in A Comparison of Eigensolvers for Large-scale 3D Modal Analysis Using AMG-Preconditioned Iterative Methods, P. Arbenz, U. L. Hetmaniuk, R. B. Lehoucq, R. S. Tuminaro, Internat. J. for Numer. Methods Engrg., 64, pp. 204-236 (2005)
• LOBPCG, a stable implementation of Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM J. Sci. Comput., 23 (2001), pp. 517-541, as described in Basis selection in LOBPCG, U. L. Hetmaniuk and R. B. Lehoucq, accepted for publication in the J. Comp. Physics.

Anasazi Contributors

The following people have contributed to the development of Anasazi:

• Chris Baker, Florida State University
• Ulrich Hetmaniuk, Sandia National Labs
• Rich Lehoucq, Sandia National Labs
• Heidi Thornquist, Sandia National Labs, hkthorn@sandia.gov

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