论文标题
Robin-Dirichlet交替迭代程序，以解决无限域中的Helmholtz方程的Cauchy问题
Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain
论文作者
论文摘要
我们考虑了在r^d，d> 2中带有n圆柱体出口的helmholtz方程的凯奇问题，并在r^{d-1}中带有有界的夹杂物。 Cauchy数据是在边界域的边界上规定的，目的是在边界的无限部分找到解决方案。 1989年，科兹洛夫（Kozlov）和马兹亚（Maz'ya）提出了一种交替的迭代方法，用于解决与椭圆形，自我接合和正定算子相关的cauchy问题。该方法的不同变体解决了与Helmholtz型操作员相关的Cauchy问题。我们考虑Mpinganzima等人提出的变体。对于有界域，并得出了无界域中过程收敛的必要条件。对于数值实现，使用有限的差异方法来解决代表截短无限条的简单矩形域中的问题。数值结果表明，通过对域的适当截断，并在适当选择罗宾参数的情况下，Robin-Dirichlet交替的迭代过程是收敛的。
We consider the Cauchy problem for the Helmholtz equation with a domain in R^d, d>2 with N cylindrical outlets to infinity with bounded inclusions in R^{d-1}. Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Maz'ya proposed an alternating iterative method for solving Cauchy problems associated with elliptic,self-adjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Mpinganzima et al. for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R^2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters, the Robin-Dirichlet alternating iterative procedure is convergent.
