This paper presents a stability-preserving model reduction method for an acoustic finite element model with perfectly matched layers (PMLs). PMLs are often introduced into an unbounded domain to simulate the Sommerfeld radiation condition. These layers act as anisotropic damping materials to absorb the scattered field, of which the material properties are frequency- and coordinate-dependent. The corresponding time-domain model size is often very large due to this frequency-dependent property and the number of elements needed per wavelength. Therefore, to enable efficient transient simulations, this paper proposes a two-step method to generate stable reduced order models (ROMs) of such systems. Firstly, the modified and stable version of PMLs is projected by a one-sided split basis, which gives a stable intermediate ROM. Secondly, the intermediate ROM is modified to satisfy the stability-preserving condition by applying the modal transformation. Applying any one-sided model order reduction method on this modified model leads to a stable and small ROM. This two-step method is further extended to account for the locally-conformal PML model by reformulating it in curvilinear coordinates, which works for arbitrary convex truncated domains. The proposed method is successfully verified by several numerical simulations.

中文翻译：

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具有完美匹配层的时域声学有限元模拟的模型降阶


本文提出了一种用于具有完美匹配层（PML）的声学有限元模型的保稳模型简化方法。 PML 通常被引入到无界域中来模拟索末菲辐射条件。这些层充当各向异性阻尼材料来吸收散射场，其材料特性与频率和坐标相关。由于这种与频率相关的特性以及每个波长所需的元件数量，相应的时域模型大小通常非常大。因此，为了实现高效的瞬态仿真，本文提出了一种两步方法来生成此类系统的稳定降阶模型（ROM）。首先，通过单侧分割基础来投影 PML 的修改稳定版本，从而给出稳定的中间 ROM。其次，通过应用模态变换对中间ROM进行修改以满足保稳条件。在此修改模型上应用任何单侧模型降阶方法都会产生稳定且较小的 ROM。通过在曲线坐标中重新表达局部共形 PML 模型，这种两步方法被进一步扩展，以解释局部共形 PML 模型，该模型适用于任意凸截断域。所提出的方法通过多次数值模拟得到了成功验证。