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| A special integration scheme for partition of unity finite element method for short wave propagation in solids |
| Revised:September 01, 2004 |
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| DOI：10.7511/jslx20064076 |
| KeyWord:short wave propagation,partition of unity finite element method,analytical integration |
| ZHOU Hao-yang LI Xi-kui |
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| Abstract: |
| A special integration scheme is developed for computing element matrices of partition of unity finite elements for short wave propagation in solids.The finite element spaces are constructed by multiplying the standard finite element shape functions referred to orthogonal coordinates,which form a partition of unity,with the local subspaces defined on the corresponding shape functions,which approximately reproduce the highly oscillatory nature of the solution and include a priori knowledge of the wave directions in each element.It is analytical for the 3,4,6,8 and 9-noded plane elements with straight edges and semi-analytical for the elements with curved edges.The numerical results exhibit a great saving in the computational efforts for the proposed integration scheme as compared with the Gauss-Legendre one. |
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