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Least squares element method for boundary eigenvalue problems
Author(s) -
Rothe Kai
Publication year - 1992
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.1620331009
Subject(s) - mathematics , eigenvalues and eigenvectors , finite element method , stiffness matrix , boundary element method , mixed finite element method , mathematical analysis , method of fundamental solutions , inverse iteration , bisection method , boundary knot method , matrix (chemical analysis) , discretization , boundary value problem , least squares function approximation , extended finite element method , structural engineering , physics , materials science , statistics , quantum mechanics , estimator , engineering , composite material
Abstract Linear and non‐linear boundary eigenvalue problems are discretized by a new finite element like method. The reason for the new construction principle is the non‐linear dependence of the dynamic stiffness element matrix on an eigenparameter. The dynamic stiffness element matrix is evaluated for a fixed number of parameters and is then elementwise replaced by a polynomial in the eigenparameter by solving least squares problems. A fast solver is introduced for the resulting non‐linear matrix eigenvalue problem. It consists of a combination of bisection method and inverse iteration. The superiority of the newconstructionprinciple in comparison with the finite or dynamic element method is demonstrated finally for some numerical examples.