Construction of the elements based on lifted multiwavelet and its applications

abstract

Lifted multiwavelet not only has the local analysis characteristics, and multi-scale, multi-resolution characteristics, but also has the flexibility property for constructing wavelet. It has shown a good prospect in solving singular problem, large gradient problem. This paper introduces lifted multiwavelet to FEM and constructs the elements based on lifted multiwavelet based on space lifting. Furthermore, the method is applied in fault diagnosis of pipe crack.

Keywords:

• Lifting scheme
• multiwavelet
• finite element
• fault diagnosis
• pipe crack

Funding

The authors acknowledge the financial support from National Natural Science Foundation of China (No. 51075314 and No. 51175399) and Natural Science Foundation of Shanxi Province (No. 2014JM7269 and No. 2014JM7267).