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Partition of unity finite element method for short wave propagation in solids

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Abstract

A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.

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Authors and Affiliations

  1. State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, P. R. China

    Li Xi-kui (Doctor) & Zhou Hao-yang

Authors
  1. Li Xi-kui
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  2. Zhou Hao-yang
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Correspondence to Li Xi-kui.

Additional information

Communicated by ZHONG Wan-xie

Project supported by the National Basic Research Program of China (973 Project) (No. 2002 CB412709) and the National Natural Science Foundation of China (Nos. 50278012, 10272027, 19832010)

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Xi-kui, L., Hao-yang, Z. Partition of unity finite element method for short wave propagation in solids. Appl Math Mech 26, 1056–1063 (2005). https://doi.org/10.1007/BF02466419

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  • DOI: https://doi.org/10.1007/BF02466419

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Chinese Library Classification

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2000 Mathematics Subject Classification

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