波散射问题的无奇性边界方程法
A Singularity-free Boundary Equation Method for Wave Scattering
摘要：
传统的边界积分方法存在格林核奇异的问题。本文以二维散射模型问题为例，导出了无奇性边界差分方程。这里，微分方程首先在规则网格上离散，然后转换为边界差分方程，而不是首先将麦克斯韦系统转换为积分边界形式，然后再离散。该程序涉及非奇异格林函数的晶格，而不是他们的奇异连续的同行。数值算例验证了该方法的有效性、准确性和收敛性。它可以推广到三维问题和其他类型的线性问题，包括声学和弹性。
英文摘要：
Traditional boundary integral methods suffer from the singularity of Green's kernels. The paper develops, for a model problem of 2D scattering as an illustrative example, singularity-free boundary difference equations. Instead of converting Maxwell's system into an integral boundary form first and discretizing second, here the differential equations are first discretized on a regular grid and then converted to boundary difference equations. The procedure involves nonsingular Green's functions on a lattice rather than their singular continuous counterparts. Numerical examples demonstrate the effectiveness, accuracy and convergence of the method. It can be generalized to 3D problems and to other classes of linear problems, including acoustics and elasticity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
