A general filter regularization method to solve the three dimensional Cauchy problem for inhomogeneous Helmholtz-type equations: Theory and numerical simulation

作者：Iran Quoc Viet; Nguyen Huy Tuan; Nguyen Van Thinh^*; Dang Duc Trong

来源：Applied Mathematical Modelling, 2014, 38(17-18): 4460-4479.

DOI：10.1016/j.apm.2014.03.001

• Cauchy problem
• Helmholtz
• Ill-posed
• Inhomogeneous source
• Regularization method

In this paper, we solve the Cauchy problem for an inhomogeneous Helmholtz-type equation with homogeneous Dirichlet and Neumann boundary condition. The proposed problem is ill-posed. Up to now, most investigations on this topic focus on very specific cases, and with Dirichlet boundary condition. Recently, we solve this problem in 20 for an inhomogeneous modified Helmholtz equation (2012). This work is a continuous expansion of our previous results. Herein we introduce a general filter regularization (GFR) method, and then from the GFR we deduce two concrete filters, which are a foundation to implement a numerical procedure. In addition, we develop a numerical model for solving this problem in three dimensional region. The proposed filter method has been verified by numerical experiments.

• 出版日期2014-9-1