A comparative study of Mur second-order absorbing boundary condition and unsplit recursive convolutional perfectly matched layer method under multi-source concurrency
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摘要: 多个激励源无延时发射(多源并发)相同中心频率脉冲会形成平面波束信号,增强数据记录质量。本文通过数值模拟对比分析在多源并发情况下,非分裂递归卷积完全匹配层作为吸收边界条件和Mur二阶吸收边界条件对电磁波的吸收效果。其研究结果表明,传统的Mur二阶吸收边界条件对多源并发、多角度掠射情况下电磁波的吸收效果不佳,在大偏移距下会造成波形畸变和形成虚假反射。而在多源并发情况下采用非分裂递归卷积完全匹配层作为吸收边界条件,将坐标伸缩因子引进时域有限差分算法中。通过傅里叶逆变换将频率域坐标伸缩变换PML方程转换到时域,对电场和磁场值在离散状态下进行递归卷积运算求解。从而避免了直接对卷积进行数值求解的复杂计算,在保证计算准确性的同时,节约了内存空间,提高了计算效率。在不分裂波场情况下,改善了网格截断位置对电磁波的吸收效果。Abstract: Plane beam signals form when multiple excitation sources simultaneously emit pulses with the same center frequency (multiple-source concurrency),thus enhancing the quality of data records.This paper compares and analyzes the electromagnetic wave absorption effects of unsplit recursive convolutional perfectly matched layer (PML) as the absorbing boundary condition and Mur second-order absorbing boundary condition under multi-source concurrency through numerical simulation.According to study results,the traditional Mur second-order absorbing boundary condition did not perform well in absorbing electromagnetic waves under the conditions of multi-source concurrency and multi-angle grazing,and it will cause waveform distortion and spurious reflections in the case of large offsets.For the unsplit recursive convolutional perfectly matched layer as the absorbing boundary condition under multi-source concurrency,coordinate scale factors were introduced into the finite-difference time-domain (FDTD) algorithm.Then,the PML equation for coordinate stretching was transformed from frequency domain into time domain through the inverse Fourier transform.Finally,the electric and magnetic field values were solved using the recursive convolution method in the discrete state,thus avoiding the complicated calculation involved in directly determining the numerical solution of convolution.This allows less memory space and high calculation efficiency while ensuring accuracy.Therefore,the unsplit recursive convolutional perfectly matched layer method improves the electromagnetic wave absorption effect at the positions where the grid terminate without inducing wave-field splitting.
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