Second-generation wavelet finite element based on the lifting scheme for GPR simulation
Feng De-Shan, Zhang Hua, Wang Xun
1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China.
2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China.
Abstract：
Ground-penetrating radar is a high-efficient, fast and non-destructive shallow surface exploration method. In order to improve the interpretation precision of detection, high-precision numerical simulation method is employed. The second-generation wavelet finite element is introduced into the forward modeling of ground penetrating radar. As the finite element basis function, the second-generation wavelet scaling function constructed by the scheme has the characteristics of multi-scale and multi-resolution. It can change the analysis scale arbitrarily according to actual needs. We can adopt small analysis scale at large gradient to improve the analysis precision, while adopt large analysis scale at small gradient to improve the analysis efficiency, which is beneficial to capture the local mutation characteristics of the solution and improve the resolution without changing mesh subdivision to realize the efficient solution of the forward GPR problem. The algorithm is applied to the numerical simulation of the line current radiation source and the tunnel non-dense lining model that have analytical solutions. The results show that the solution results of the second-generation wavelet finite element are in good agreement with the analytical solutions and the conventional finite element solutions, which verify the correctness of the second-generation wavelet finite element algorithm. Besides, the second-generation wavelet finite element algorithm can change the analysis scale arbitrarily according to the actual problem without subdividing grids again. The adaptive algorithm is superior to traditional scheme in grid refinement and order raise, which is especially suitable for solving complex GPR forward modeling problems with large gradient and singularity.
2018, Vol. 15 
