Abstract Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs, with the appropriate number of terms, to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained. A detailed construction of these DC finite difference schemes is presented. Additionally, a rigorous proof of the consistency of the DC schemes with the Helmholtz equation and the ABCs in polar coordinates is also given. The results of several numerical experiments corroborate the high order convergence of the novel method.

中文翻译：

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声学散射的高阶方法：将远场扩展 ABC 与延迟校正方法耦合

摘要 构造了最初定义在无界域上的时谐声散射问题的任意高阶数值方法。这是通过将最近开发的高阶局部吸收边界条件 (ABC) 与亥姆霍兹方程的有限差分方法相结合来完成的。这些 ABC 是基于通过远场扩展对出射波的精确表示。有限差分方法由延迟校正 (DC) 技术构建而成，使用适当的项数将亥姆霍兹方程和 ABC 近似为任何所需的阶数。结果，获得了总收敛阶数等于DC方案阶数的高阶数值方法。介绍了这些 DC 有限差分方案的详细构造。此外，还给出了 DC 方案与 Helmholtz 方程和极坐标 ABC 一致性的严格证明。几个数值实验的结果证实了新方法的高阶收敛性。