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Eigenvalue translation method for stabilizing an unsymmetric Lanczos reduction process
Author(s) -
Li Henian,
Woodbury Allan,
Aitchison Peter
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980930)43:2<221::aid-nme424>3.0.co;2-x
Subject(s) - eigenvalues and eigenvectors , mathematics , discretization , finite element method , lanczos resampling , mathematical analysis , reduction (mathematics) , geometry , physics , quantum mechanics , thermodynamics
The Unsymmetric Lanczos Reduction method has been recently developed to reduce the size of a large‐scale linear system which is the discretized form of a time‐dependent partial differential equation problem with a large physical domain. This has been applied to solve the time‐dependent advection–dispersion equation discretized by finite element or finite difference methods. However, the reduced system sometimes suffers time instability because of relocation of the approximate eigenvalues into the left half plane. This paper develops a method for stabilizing the reduced system while preserving the accuracy of the solution. The unstable eigenvalues are translated from the left half complex plane to the right half, leaving eigenvalues in right half plane unchanged. The results of numerical simulations of the synthetic and practical field contaminant transport problems show the efficiency and accuracy of this method. © 1998 John Wiley & Sons, Ltd.