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67 lines
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<!-- DO NOT EDIT: this is a cleared public file -->
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<HEAD><TITLE>PeIGS</TITLE></HEAD>
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<BODY BACKGROUND="pinkpig3.jpg" BGCOLOR="FAEBD7">
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<UL>
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<LI><A HREF="../../nwchem.html">Return to NWchem home page</A>
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</LI></UL><HR>
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<H1>PeIGS - Parallel Eigensolver</H1>
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<H2>George I. Fann and Richard J. Littlefield</H2>
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<P> Our parallel eigensolver package is called PeIGS, and solves the
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standard and generalized, real, symmetric eigenproblems. It is based
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on bisection for eigenvalues and repeated inverse iteration and
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reorthogonalization for eigenvectors. The parallel performance is
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competitive with alternative methods for typical "chemical" problem sizes, and is
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illustrated with three applications from quantum chemistry
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<UL>
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<LI> SCF-Hartree-Fock (Fock matrix for 389 atom zeolite fragment, 2053 functions)
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<LI> density functional theory (charge-fitting matrix for <I>(SiOSi)6</I>, 1687)
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<LI> resolution-of-the-identity Moller-Plesset theory (biphenyl
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charge-fitting matrix, 966)
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</UL>
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The distinguishing feature of the repeated inverse iteration and
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orthonormalization method used by PeIGS is that orthogonalization is
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performed across multiple processors as dictated by the spectrum.
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The correct, orthonormal result is <I>always</I> generated.
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<P>For a spectrum that is well spaced, there is essentially no
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orthogonalization time. Most of the time is consumed in the
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Householder reduction to tridiagonal form. For large numerically
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degenerate clusters, almost all of the time is consumed in the
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Householder reduction and in orthonormalization.
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<P><IMG SRC="qc_speedup.gif">
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<P><IMG SRC="qc_times.gif">
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<H2>Acknowledgments</H2>
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<P>This work was performed under the auspices of the High Performance
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Computing and Communications Program of the Office of Scientific
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Computing, U.S. Department of Energy under contract DE-AC6-76RLO 1830
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with Battelle Memorial Institute which operates the Pacific Northwest
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National Laboratory, a multiprogram national laboratory. This work
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has made extensive use of software developed by the Molecular Science
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Software Group of the Environmental Molecular Sciences Laboratory
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project managed by the Office Health and Energy Research.
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<P>This research was performed in part using the Caltech Concurrent
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Supercomputing Facilities (CCSF) operated by Caltech on behalf of the
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Concurrent Supercomputing Consortium. Access to this facility was
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provided by Pacific Northwest National Laboratory.
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<P>
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<HR>
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<ADDRESS>Prepared by RJ Harrison: Email: nwchem-support@emsl.pnl.gov.</ADDRESS>
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