Premium
Diagonalization procedure for scaled boundary finite element method in modeling semi‐infinite reservoir with uniform cross‐section
Author(s) -
Li S. M.
Publication year - 2009
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.2647
Subject(s) - eigenvalues and eigenvectors , finite element method , mathematics , diagonal , boundary (topology) , matrix (chemical analysis) , stiffness matrix , diagonalizable matrix , mathematical analysis , symmetric matrix , geometry , structural engineering , physics , engineering , materials science , quantum mechanics , composite material
To improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam–reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross‐section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi‐infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity. Copyright © 2009 John Wiley & Sons, Ltd.