A general filter regularization method to solve the three dimensional Cauchy problem for inhomogeneous Helmholtz-type equations: Theory and numerical simulation |
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Institution: | 1. Department of Civil and Environmental Engineering, Seoul National University, Republic of Korea;2. Institute for Computational Science and Technology at Ho Chi Minh City, Viet Nam;3. Department of Mathematics, University of Science, Vietnam National University at Ho Chi Minh City, Viet Nam |
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Abstract: | 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 2D 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. |
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Keywords: | Cauchy problem Helmholtz Ill-posed Inhomogeneous source Regularization method |
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