有限元时域模拟中阻尼层的自动校准
Automatic calibration of damping layers in finite element time domain simulations
AI总结：
本文提出一种基于优化方法自动校准匹配层的流程，通过求解受偏微分方程约束的优化问题，利用分段常数衰减函数提高效率，并引入连续匹配层替代完美匹配层，减少计算成本。
摘要：
匹配层常用于波动传播数值模拟中以建模（半）无限域。衰减函数描述层中的阻尼，并提供在感兴趣域与吸收区域界面处的波阻抗匹配。在衰减函数中选择参数是非平凡的。本文提出了一种优化程序，用于自动校准匹配层。该程序基于求解受偏微分方程约束的优化问题，使用多项式和分段常数衰减函数。我们实验表明，对于有限元时域模拟，分段常数衰减函数至少与二次衰减函数一样高效。这一观察导致我们引入连续匹配层作为完美匹配层的替代方案，可以轻松用于具有任意几何形状的问题。此外，使用连续匹配层相比完美匹配层可减少计算成本。展示了声学、弹性动力学和电磁学问题的例子。使用FEniCS/DOLFIN和dolfin-adjoint库进行数值模拟，并且所有数值示例的计算机代码免费提供。
英文摘要：
Matched layers are commonly used in numerical simulations of wave propagation to model (semi-)infinite domains. Attenuation functions describe the damping in layers, and provide a matching of the wave impedance at the interface between the domain of interest and the absorbing region. Selecting parameters in the attenuation functions is non-trivial. In this work, an optimisation procedure for automatically calibrating matched layers is presented. The procedure is based on solving optimisation problems constrained by partial differential equations with polynomial and piecewise-constant attenuation functions. We show experimentally that, for finite element time domain simulations, piecewise-constant attenuation function are at least as efficient as quadratic attenuation functions. This observation leads us to introduce consecutive matched layers as an alternative to perfectly matched layers, which can easily be employed for problems with arbitrary geometries. Moreover, the use of consecutive matched layers leads to a reduction in computational cost compared to perfectly matched layers. Examples are presented for acoustic, elastodynamic and electromagnetic problems. Numerical simulations are performed with the libraries FEniCS/DOLFIN and dolfin-adjoint, and the computer code to reproduce all numerical examples is made freely available.
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