Multiple scale finite element methods

Wing Kam Liu*, Yan Zhang, Martin R. Ramirez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)969-990
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
StatePublished - Oct 5 1991

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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