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首页> 外文期刊>Engineering analysis with boundary elements >Topological Sensitivity And Fmm-accelerated Bem Applied To 3d Acoustic Inverse Scattering
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Topological Sensitivity And Fmm-accelerated Bem Applied To 3d Acoustic Inverse Scattering

机译：拓扑灵敏度和Fmm加速Bem在3d声学逆散射中的应用

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摘要

This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving the free field and an adjoint field associated with the cost function. These fields are computed by means of a boundary element formulation accelerated by the fast multipole method. A computationally fast approach for performing a global preliminary search based on the available overspecified boundary data is thus defined. Its usefulness is demonstrated through results of numerical experiments on the qualitative identification of hard obstacles in a bounded 3D acoustic domain, for configurations featuring O(10~5) nodal unknowns and O(10~6) sampling points, based on exact or noisy synthetic data.
机译：这项研究是在标量（例如声波）反散射的框架内进行的。提出了一种基于成本函数的拓扑敏感性分布的定性探测技术，该成本函数与反问题相关的无限小的硬障碍物的形核有关。灵敏度分布表示为包含与成本函数关联的自由场和伴随场的双线性公式。这些场是通过快速多极方法加速的边界元素公式计算的。因此，定义了一种基于计算的快速方法，用于基于可用的过分指定的边界数据执行全局初步搜索。通过对有限3D声域中的硬障碍进行定性鉴定的数值实验结果证明了其有用性，该结构基于精确或嘈杂的合成，具有O（10〜5）节点未知和O（10〜6）采样点的配置数据。

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