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Multi-scale finite element analysis of acoustic waves using global residual-free meshfree enrichments

C.T. Wu, Wei Hu
2013 Interaction and multiscale mechanics  
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
more » ... 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.
doi:10.12989/imm.2013.6.2.083 fatcat:zwkzc7wfejfpfcakxthxhcn6um