JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices

A new software code for computing selected eigenvalues and associated eigenvectors of a real symmetric matrix is described. The eigenvalues are either the smallest or those closest to some specified target, which may be in the interior of the spectrum. The underlying algorithm combines the Jacobi–Davidson method with efficient multilevel incomplete LU (ILU) preconditioning. Key features are modest memory requirements and robust convergence to accurate solutions. Parameters needed for incomplete LU preconditioning are automatically computed and may be updated at run time depending on the convergence pattern. The software is easy to use by non-experts and its top level routines are written in FORTRAN 77. Its potentialities are demonstrated on a few applications taken from computational physics.Program summaryProgram title: JADAMILUCatalogue identifier: ADZT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZT_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 101 359No. of bytes in distributed program, including test data, etc.: 7 493 144Distribution format: tar.gzProgramming language: Fortran 77Computer: Intel or AMD with g77 and pgf; Intel EM64T or Itanium with ifort; AMD Opteron with g77, pgf and ifort; Power (IBM) with xlf90.Operating system: Linux, AIXRAM: problem dependentWord size: real:8; integer: 4 or 8, according to user's choiceClassification: 4.8Nature of problem: Any physical problem requiring the computation of a few eigenvalues of a symmetric matrix.Solution method: Jacobi–Davidson combined with multilevel ILU preconditioning.Additional comments: We supply binaries rather than source code because JADAMILU uses the following external packages:
• MC64. This software is copyrighted software and not freely available. COPYRIGHT (c) 1999 Council for the Central Laboratory of the Research Councils.
• AMD. Copyright (c) 2004–2006 by Timothy A. Davis, Patrick R. Amestoy, and Iain S. Duff. All Rights Reserved. Source code is distributed by the authors under the GNU LGPL licence.
• BLAS. The reference BLAS is a freely-available software package. It is available from netlib via anonymous ftp and the World Wide Web.
• LAPACK. The complete LAPACK package or individual routines from LAPACK are freely available on netlib and can be obtained via the World Wide Web or anonymous ftp.
• For maximal benefit to the community, we added the sources we are proprietary of to the tar.gz file submitted for inclusion in the CPC library. However, as explained in the README file, users willing to compile the code instead of using binaries should first obtain the sources for the external packages mentioned above (email and/or web addresses are provided).Running time: Problem dependent; the test examples provided with the code only take a few seconds to run; timing results for large scale problems are given in Section 5.