Ground-penetrating radar (GPR) is a highly efficient, fast and non-destructive exploration method for shallow surfaces. High-precision numerical simulation method is employed to improve the interpretation precision of detection. Second-generation wavelet finite element is introduced into the forward modeling of the GPR. As the finite element basis function, the second-generation wavelet scaling function constructed by the scheme is characterized as having multiple scales and resolutions. The function can change the analytical scale arbitrarily according to actual needs. We can adopt a small analysis scale at a large gradient to improve the precision of analysis while adopting a large analytical scale at a small gradient to improve the efficiency of analysis. This approach 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 line current radiation source and tunnel non-dense lining model with analytical solutions. Result show that the solution results of the second-generation wavelet finite element are in agreement with the analytical solutions and the conventional finite element solutions, thereby verifying the accuracy of the second-generation wavelet finite element algorithm. Furthermore, 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 basis function order increase, which makes this algorithm suitable for solving complex GPR forward-modeling problems with large gradient and singularity.

中文翻译：

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基于提升方案的第二代小波有限元的GPR仿真

探地雷达（GPR）是一种用于浅层表面的高效，快速且无损的探测方法。采用高精度数值模拟方法提高了检测结果的解释精度。第二代小波有限元被引入到GPR的正向建模中。该方案构造的第二代小波缩放函数作为有限元基函数，具有多个尺度和分辨率。该功能可以根据实际需要任意改变分析规模。我们可以采用大梯度的小分析规模来提高分析的精度，而采用小梯度的大分析规模来提高分析的效率。这种方法有利于捕获解决方案的局部突变特征，并在不更改网格细分的情况下提高分辨率，从而实现正向GPR问题的有效解决方案。将该算法应用于具有解析解的线电流辐射源和隧道非密衬模型的数值模拟。结果表明，第二代小波有限元的求解结果与解析解和常规有限元解相吻合，从而验证了第二代小波有限元算法的准确性。此外，第二代小波有限元算法可以根据实际问题任意改变分析尺度，而无需再次细分网格。