Serkh Kirill, Rokhlin Vladimir
Department of Mathematics, Yale University, New Haven, CT 06511
Proc Natl Acad Sci U S A. 2016 Aug 16;113(33):9171-6. doi: 10.1073/pnas.1609578113. Epub 2016 Aug 1.
In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.
在本文中,我们求解了多边形区域上亥姆霍兹方程的几个边值问题。我们观察到,当这些问题被表述为势理论的边界积分方程时,解可以用适当选取的贝塞尔函数级数来表示。除了在解析上清晰明了外,所得表达式还便于构建精确且高效的数值算法。通过一些数值例子对结果进行了说明。