论文标题
klein-gordon奇异波导的积分公式
Integral formulation of Klein-Gordon singular waveguides
论文作者
论文摘要
我们考虑对在两个空间维度中分离绝缘阶段的奇异波导的分析。绝缘域是通过沿巨大的schrödinger方程和奇异波导建模的，该波导沿沿分隔绝缘体的一维界面沿着适当的跳跃条件进行建模。我们提出了问题的整体公式，并分析其数学特性。我们还实现了一种快速的多极和扫描的迭代算法来求解积分方程，并以数值证明了该方法的快速收敛性。解决方案和散射效应的几个数值示例说明了我们的理论。
We consider the analysis of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schrödinger equation and the singular waveguide by appropriate jump conditions along the one-dimensional interface separating the insulators. We present an integral formulation of the problem and analyze its mathematical properties. We also implement a fast multipole and sweeping-accelerated iterative algorithm for solving the integral equations, and demonstrate numerically the fast convergence of this method. Several numerical examples of solutions and scattering effects illustrate our theory.
