一种算子自定义小波薄板单元及应用

提出了基于提升方案的自适应算子自定义小波有限元法,构造了一种新的算子自定义小波薄板单元。建立二维Hermite型有限元多分辨空间和两尺度关系,并由广义变分原理推导薄板结构关于尺度函数和小波函数的内积关系式,即算子。为满足算子正交性,提出基于提升方案的算子自定义小波单元的构造方法,其优点在于可根据问题的需要来设计具有期望特性的小波基。提出基于两尺度误差的自适应算子自定义小波有限元方法,通过向大于误差阈值的局域添加算子自定义小波,实现薄板结构问题的高效求解。算子自定义小波有限元法节省了重新划分网格或提高插值函数的阶次所带来的大量有限元前处理时间,并且实现薄板问题的高效解耦运算。

An operator custom-design wavelet-based thin plate element and its application

An adaptive operator custom-design wavelet finite element method based on the lifting scheme is proposed and a new operator custom-design wavelet thin plate element is constructed.A two-dimensional Hermite-type multiresolution finite element space and two-level relation are built.The inner production equation of scaling functions and wavelet functions of thin plate structure,also called the operator,is derived based on the general variational principle.The construction method of operator custom-design wavelet finite elements based on the lifting scheme is presented to meet the operator-orthogonalization.The property of the method is that the wavelets can be designed with the specified feature depending on the requirements of the problems.An adaptive operator custom-design wavelet finite element method is presented on the two-level error estimation,which can solve the thin plate problems efficiently by adding operator custom-design wavelets into the local domains higher than the threshold value.The operator custom-design wavelet finite element method saves a great deal of preprocessing time of refining the meshes or increasing the approximating order of the interpolating functions and realizes efficient decoupling computation of thin plate problems.