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A parallel eigenvalue problem solver for computational nanoelectronics
Author(s) -
Naumov Maxim,
Sameh Ahmed
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700685
Subject(s) - eigenvalues and eigenvectors , hermitian matrix , solver , divide and conquer eigenvalue algorithm , convergence (economics) , mathematics , chebyshev polynomials , quadratic equation , chebyshev filter , speedup , mathematical analysis , physics , computer science , mathematical optimization , pure mathematics , geometry , parallel computing , quantum mechanics , economics , economic growth
A new parallel eigenvalue solver for finding the interior eigenvalues of a standard Hermitian eigenvalue problem arising in atomistic simulations in nanoelectronics is presented. It is based on the Tracemin algorithm which finds the p smallest eigenpairs of a generalized Hermitian eigenvalue problem. The original problem is modified using spectrum folding or a quadratic mapping so that the interior eigenvalues are mapped onto the smallest or the largest, respectively. In the latter case the solution of systems in every iteration of Tracemin is avoided and Chebyshev polynomials are used to speedup convergence. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)