声散射的高阶方法：耦合远场展开ABC与延迟校正方法
High order methods for acoustic scattering: Coupling Farfield Expansions ABC with Deferred-Correction methods
摘要：
构造了求解无界区域上时谐声散射问题的任意高阶数值方法。这是通过耦合最近开发的高阶局部吸收边界条件（ABC）与有限差分法的Helmholtz方程。这些ABC是基于通过远场展开的出射波的精确表示。有限差分法，这是从延迟校正（DC）技术构造，近似亥姆霍兹方程和ABC，与适当的数目的条款，以任何所需的顺序。其结果是，高阶数值方法的总阶的收敛等于DC格式的顺序得到。这些DC有限差分格式的详细建设。此外，还严格证明了DC格式与Helmholtz方程和ABC格式在极坐标下的一致性。数值实验的结果证实了新方法的高阶收敛性。
英文摘要：
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.
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