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An algebraic multigrid wave–ray algorithm to solve eigenvalue problems for the helmholtz operator
Author(s) -
Livshits Irene
Publication year - 2004
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.379
Subject(s) - multigrid method , helmholtz equation , helmholtz free energy , mathematics , eigenvalues and eigenvectors , solver , operator (biology) , algebraic number , variable (mathematics) , mathematical analysis , partial differential equation , mathematical optimization , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , boundary value problem
Helmholtz equations with variable coefficients are known to be hard to solve both analytically and numerically. In this paper, we introduce a numerical multigrid solver for one‐dimensional Helmholtz eigenvalue problems with periodic potentials and solutions. The solvers employ wave–ray methodology suggested by Brandt, Livshits for Helmholtz equations with constant coefficients. The paper concludes with numerical experiments and the discussion of future efforts for solving two‐dimensional problems. Copyright © 2004 John Wiley & Sons, Ltd.