Modeling long‐range propagation of electromagnetic waves is necessary to study the performance of systems, for applications such as radar or navigation. Such models generally rely on split‐step Fourier (SSF) because large mesh sizes can be used. The split‐step wavelet method (SSW) is a recently developed method allowing to perform the same simulations as with SSF but in a shorter computation time. This method requires the pre‐computation of a free‐space propagator. Up to now, one limitation of SSW is that the steps must remain constant during the propagation. In this study, we propose an improvement of SSW in terms of memory size and versatility. This improvement relies on the use of a set of propagators, that is, the propagation of elementary wavelets. The limited support of wavelets renders the computation of the set of propagators fast, approximately as fast as one step of propagation with SSW. First, a numerical test shows the advantage in terms of computation time. Second, a numerical experience shows the advantage in terms of memory. Finally, the SSW method is applied as the direct method for a radio occultation configuration.

中文翻译：

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用于二维远距离传播仿真的局部分裂小波方法

对电磁波的远距离传播进行建模，对于研究系统的性能（例如雷达或导航）是必要的。此类模型通常依赖于分步傅里叶（SSF），因为可以使用较大的网格。分段小波方法（SSW）是最近开发的一种方法，可以执行与SSF相同的仿真，但计算时间较短。此方法需要对自由空间传播器进行预计算。到目前为止，SSW的一个局限性在于，在传播过程中步长必须保持恒定。在这项研究中，我们建议在内存大小和多功能性方面改进SSW。这种改进依赖于使用一组传播子，即基本小波的传播。小波的有限支持使传播子集的计算速度更快，大约与SSW传播的一个步骤一样快。首先，数值测试显示了在计算时间方面的优势。其次，数字经验显示出在内存方面的优势。最后，将SSW方法用作无线电掩星配置的直接方法。