论文标题
用于前向和反随机声散射的等几何多级正交
Isogeometric multilevel quadrature for forward and inverse random acoustic scattering
论文作者
论文摘要
我们使用快速的同一几乎级的边界元素方法研究了通过在三维空间中随机形状的障碍物来研究正向和反声散射问题的数值解。在等几何框架内，可以通过简单地更新代表散点子的NURBS映射来有效地计算随机散射器的实现。这样，我们最终得到了一个随机变形字段。特别是，我们表明，对变形场在散射器表面的期望和协方差的了解已经足以计算表面Karhunen-Loève扩展。在利用同几年框架上，我们利用多级正交方法有效地近似关注的量，例如分散的波浪的期望和方差。在封闭随机障碍物的人造固定界面上计算波浪的cauchy数据，我们还可以直接推断自由空间中的兴趣数量。采用贝叶斯范式，我们最终从人工界面的散射波的嘈杂测量值中计算出散射器的预期形状和方差。给出了前进和反问题的数值结果，以证明所提出的方法的可行性。
We study the numerical solution of forward and inverse acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations of the random scatterer can efficiently be computed by simply updating the NURBS mappings which represent the scatterer. This way, we end up with a random deformation field. In particular, we show that the knowledge of the deformation field's expectation and covariance at the surface of the scatterer are already sufficient to compute the surface Karhunen-Loève expansion. Leveraging on the isogeometric framework, we utilize multilevel quadrature methods for the efficient approximation of quantities of interest, such as the scattered wave's expectation and variance. Computing the wave's Cauchy data at an artificial, fixed interface enclosing the random obstacle, we can also directly infer quantities of interest in free space. Adopting the Bayesian paradigm, we finally compute the expected shape and the variance of the scatterer from noisy measurements of the scattered wave at the artificial interface. Numerical results for the forward and inverse problem are given to demonstrate the feasibility of the proposed approach.
