This paper introduces an innovative numerical methodology designed to achieve high precision solution of acoustic wave propagation problem in isotropic material. During the temporal discretization process, the Krylov deferred correction (KDC) technique is employed, wherein a new variable is introduced to handle the second-order time derivative in the governing equations. An improved strategy is adopted for precisely implementing boundary conditions. Following this, the arbitrary-order generalized finite difference method (GFDM) is employed to simulate the transformed boundary value problem at each time step, enabling our framework to select the Taylor series expansion order arbitrarily. Ultimately, a hybrid numerical approach for wave problems is developed to achieve arbitrary-order accuracy in both spatial and temporal approximations. The developed scheme undergoes validation through four different numerical experiments in two- or three-dimension, wherein the numerical solutions obtained are compared with either analytical solutions or results from COMSOL software.

中文翻译：

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使用空间和时间近似中具有任意阶精度的混合方法对波传播进行数值模拟


本文介绍了一种创新的数值方法，旨在实现各向同性材料中声波传播问题的高精度求解。在时间离散化过程中，采用了克雷洛夫递延校正（KDC）技术，其中引入一个新变量来处理控制方程中的二阶时间导数。采用改进的策略来精确实现边界条件。接下来，采用任意阶广义有限差分法（GFDM）来模拟每个时间步的变换边值问题，使我们的框架能够任意选择泰勒级数展开阶数。最终，开发了一种用于波浪问题的混合数值方法，以在空间和时间近似上实现任意阶精度。所开发的方案通过四个不同的二维或三维数值实验进行验证，其中获得的数值解与解析解或 COMSOL 软件的结果进行比较。