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Lanczos method for heat conduction analysis
Author(s) -
NourOmid Bahram
Publication year - 1987
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/nme.1620240117
Subject(s) - lanczos resampling , thermal conduction , lanczos algorithm , mathematics , generalized minimal residual method , krylov subspace , matrix (chemical analysis) , algorithm , mathematical optimization , eigenvalues and eigenvectors , physics , iterative method , thermodynamics , chemistry , quantum mechanics , chromatography
An analysis technique that uses the Lanczos vectors to construct a Reyleigh–Ritz solution for the transient heat conduction problem is presented. The Lanczos vectors are derived from the heat supply vector and incorporate all the information peculiar to a given problem. They are orthonormal with respect to the heat capacitance matrix and are generated with a minimum of computational effort. Furthermore, an error bound is derived that can be used to terminate the Lanczos algorithm as soon as the number of vectors required to obtain a desired degree of accuracy has been generated. A summary of the algorithm is presented and the accuracy and efficiency of the method is illustrated using a numerical example.
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