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Matrix‐Padé via Lanczos solutions for vibrations of fluid–structure interaction
Author(s) -
Liew HawLing,
Pinsky Peter M.
Publication year - 2010
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.2936
Subject(s) - lanczos resampling , lanczos algorithm , krylov subspace , matrix (chemical analysis) , mathematics , finite element method , projection (relational algebra) , padé approximant , boundary value problem , field (mathematics) , vibration , subspace topology , mathematical analysis , algorithm , eigenvalues and eigenvectors , structural engineering , physics , pure mathematics , engineering , linear system , materials science , quantum mechanics , composite material
For multiple‐frequency full‐field solutions of the boundary value problem describing small fluid–structure interaction vibration superimposed on a nominal state with prestress, we propose an efficient reduced order method by constructing the full‐field matrix‐Padé approximant of its finite element matrix function. Exploiting the matrix‐Padé via Lanczos connection, the Padé coefficients are computed in a stable and efficient way via an unsymmetric, banded Lanczos process. The full‐field Padé‐type approximant is the result of one‐sided projection onto Krylov subspace, we established its order of accuracy, which is not maximal. The superiority of this method in terms of various problem dimensions and parameters is established by complexity analysis via flop counts. Numerical examples obtained by using a model problem verified the accuracy of this full‐field matrix‐Padé approximant. Copyright © 2010 John Wiley & Sons, Ltd.