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Interaction and Multiscale Mechanics
  Volume 6, Number 2, June 2013 , pages 83-105
 open access

Multi-scale finite element analysis of acoustic waves using global residual-free meshfree enrichments
C.T. Wu and Wei Hu

    In this paper, a multi-scale meshfree-enriched finite element formulation is presented for the analysis of acoustic wave propagation problem. The scale splitting in this formulation is based on the Variational Multi-scale (VMS) method. While the standard finite element polynomials are used to represent the coarse scales, the approximation of fine-scale solution is defined globally using the meshfree enrichments generated from the Generalized Meshfree (GMF) approximation. The resultant fine-scale approximations satisfy the homogenous Dirichlet boundary conditions and behave as the \"global residual-free\" bubbles for the enrichments in the oscillatory type of Helmholtz solutions. Numerical examples in one dimension and two dimensional cases are analyzed to demonstrate the accuracy of the present formulation and comparison is made to the analytical and two finite element solutions.
Key Words
    acoustic; multi-scale; finite element; Helmholtz; meshfree
C.T. Wu and Wei Hu : Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA

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