Acoustic simulation in frequency-domain is related to solving Helmholtz equations, which is still highly challenging at high frequency with complex geometries. In this paper, a learning based numerical method (LbNM) is proposed for general boundary value problems of Helmholtz equation. By using Tikhonov regularization, the solution operator is stably learned from various data solutions especially fundamental solutions. The reconstructed solution operator is reusable and enables fast solution updating with new boundary inputs. The present method is featured by strong interpretability and generalizability. Numerical results demonstrate advantages in precision and efficiency. It can be applied to various engineering problems such as cabin acoustic simulations flexibly.

中文翻译：

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基于学习的高频声频域仿真数值方法

频域声学仿真与求解亥姆霍兹方程有关，这在具有复杂几何形状的高频下仍然具有挑战性。本文针对亥姆霍兹方程的一般边值问题提出了一种基于学习的数值方法（LbNM）。通过使用吉洪诺夫正则化，解算子可以从各种数据解尤其是基本解中稳定地学习。重建的解算子是可重用的，并且能够使用新的边界输入快速更新解。该方法具有较强的可解释性和普适性。数值结果显示了精度和效率方面的优势。可灵活应用于舱室声学仿真等多种工程问题。