AI 中文总结
研究如何将声场数据从源区域平移到目标区域，核心方法是将场数据表示为球面上的球谐展开，利用基尔霍夫 - 亥姆霍兹积分通过“点射”法轴向平移，用于时域快速多极子方法，计算量约与\(N^{2}\)成比例且收敛到六位数字。
AI 中文摘要
本文提出一种将声场数据从源区域平移到目标区域的方法。场数据分别表示为围绕源区域和目标区域的球面上的球谐展开，利用基尔霍夫 - 亥姆霍兹积分通过“点射”法进行轴向平移，从一个球面平移到另一个球面。该方法主要用于时域快速多极子方法，并给出了反映此应用的测试案例。对于合适的参数值，该方法收敛到六位数字，计算量约与\(N^{2}\)成比例，其中\(N\)是场数据的球谐展开阶数。
英文摘要
A method is presented for the translation of acoustic field data from a source to a target region. Field data are represented as spherical harmonic expansions on spheres surrounding the source and target regions respectively and expansions are translated using a ``point and shoot'' method using the Kirchhoff--Helmholtz integral to carry out an axial translation from one sphere to the other. The principal motivation for the method is its use in a time-domain Fast Multipole Method, and test cases reflective of this application are presented. The method converges to six digits for appropriate values of parameters and for the values of $N$ considered here computational effort scales approximately as $N^{2}$ where $N$ is the order of spherical harmonic expansion for the field data. The method is causal and thus avoids artifacts generated in methods which are not based on intrinsically causal formulations.
