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Multiple scale finite element methods
Author(s) -
Liu Wing Kam,
Zhang Yan,
Ramirez Martin R.
Publication year - 1991
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.1620320504
Subject(s) - finite element method , discretization , spectral element method , temporal discretization , convergence (economics) , scale (ratio) , spectral method , rate of convergence , mixed finite element method , finite difference , mathematics , extended finite element method , spacetime , algorithm , computer science , mathematical optimization , mathematical analysis , physics , computer network , channel (broadcasting) , quantum mechanics , economics , thermodynamics , economic growth
New temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems. To satisfy the spatial counterpart of the requirement on time step constraint, finite‐spectral elements and finite wave elements are developed. Finite‐spectral element methods combine the usual finite elements with the fast convergent spectral functions to obtain a faster convergence rate; whereas, finite wave elements are developed in parallel to the temporal shifting technique. Therefore, the spatial resolution is increased substantially. These methods are especially applicable to structural acoustics and linear space structures. Numerical examples are presented to illustrate the effectiveness of these methods.