Analysis of continuous formulations underlying the computation of time-harmonic acoustics in exterior domains
Analysis of continuous formulations underlying the computation of time-harmonic acoustics in exterior domains
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DOI：
10.1016/0045-7825(92)90109-w
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发表时间：
1992-05
期刊：
影响因子：
--
通讯作者：
I. Harari;T. Hughes
中科院分区：
文献类型：
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作者：
I. Harari;T. Hughes
潜在的非唯一性边界表示的亥姆霍兹方程强调了调查连续的基于边界和基于域的配方，这是这项工作的主要目的的重要性。讨论了边界积分方程解的唯一性。我们分析配方的域为基础的计算所得出的DtN方法，它强加了一个人工边界上的函数和它的正常导数之间的关系。DtN制定具有非反射边界条件，并产生精确的（从而唯一的）解决方案。在实际实现中，DtN映射经常被截断。截断的DtN算子不能完全抑制高次模的反射，导致高次谐波特征波数处的唯一性丧失。然而，简单的表达式，确定了足够数量的条款在运营商的唯一解决方案在任何给定的波数。我们证明了一个局部近似的边界条件恢复所有波数的唯一性，并推导出其三维版本。
Potential non-uniqueness of boundary representations of the Helmholtz equation underscores the importance of investigating continuous boundary-based and domain-based formulations, which is the main purpose of this work. Uniqueness properties of the solutions of boundary integral equations are reviewed. We analyze formulations for domain-based computation that are derived by the DtN method, which imposes a relation between the function and its normal derivative on an artificial boundary. The DtN formulation is shown to possess non-reflective boundary conditions and to give rise to exact (and thereby unique) solutions. In practical implementation the DtN map is often truncated. The truncated DtN operator fails to completely inhibit reflection of higher modes, resulting in loss of uniqueness at characteristic wave numbers of higher harmonics. However, simple expressions that determine a sufficient number of terms in the operator for unique solutions at any given wave number are derived. We prove that a local approximation of the boundary conditions restores uniqueness for all wave numbers, and derive its three-dimensional version.