科研之友
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摘要
Based on the separable wavelet theory, we construct the two-dimensional Daubechies wavelet bases by means of one-dimensional Daubechies scaling functions, which is used for interpolation functions of solving the GPR wave equation, thus present the discrete format of two-dimensional Daubechies wavelet finite element GPR equation. By introducing a transformation matrix, the transformation between the wavelet coefficient space and the GPR electromagnetic field is implemented. By introducing the degree of freedom condensation technique, it effectively solves the problem of too much freedom in internal wavelet unit during the solution process of the wavelet finite element, reducing the amount of calculation and can be coupled easily with traditional finite element method. Then the calculation formulas of connection coefficient used in Daubechies wavelet finite element are elaborated, which effectively resolve the difficulty and core problem in solving partial differential equations by wavelet finite element. Finally, with two typical GPR models as example, comparing the radar forward sections and the single waveforms between Daubechies wavelet finite element method and the traditional finite element method, and the result shows that under the conditions of the same dividing method and the number of nodes, the compact support and orthogonality of Daubechies wavelet finite element improves the solving efficiency to some extent, and it can be fitted well with the solving result of finite element method, validating the correctness of the Daubechies wavelet finite element method, which provides a new idea for solving the GPR wave equation.
