Discrete artificial boundary conditions for transient scalar wave propagation in a 2D unbounded layered media |
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| Affiliation: | 1. University of Cagliari, DICAAR – Department of Civil and Environmental Engineering and Architecture, 2, via Marengo, I-09123 Cagliari, Italy;2. Technische Universität Dresden, Institut Statik und Dynamik der Tragwerke, D-01062 Dresden, Germany;1. Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany;2. University of Belgrade, Bulevar kralja Aleksandra 73, 11000, Belgrade, Serbia;1. School of Civil Engineering, Sun Yat-sen University, No. 135, Xingang Xi Road, Guangzhou 510275, PR China;2. School of Architectural Engineering, Guangzhou Institute of Science and Technology, No. 638, Xingtai Third Road, Taihe Town, Baiyun District, Guangzhou 510540, China;3. School of Civil and Transportation Engineering, Guangdong University of Technology, No. 100, Waixihuan Road, University Town, Panyu District, Guangzhou 510006, PR China;1. MOE Key Laboratory of New Technology for Construction of Cities in Mountain Area and School of Civil Engineering, Chongqing University, Chongqing 400045, China;2. National Center for Research on Earthquake Engineering, Taipei 106, Taiwan |
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| Abstract: | This paper presents an efficient numerical method for direct time-domain solution of the transient scalar wave propagation in a two-dimensional unbounded multi-layer soil. The unbounded domain is truncated by an artificial boundary which demands the corresponding boundary conditions. In the new approach, only the artificial boundary is discretized into one-dimensional finite elements, yielding a new time-dependent partial differential equation (PDE) for displacements with respect to only one spatial coordinate. Factorization of the PDE and introduction of the residual radiation functions, there results a linear first-order ordinary differential equation (ODE). Its stability is ensured. The time-dependent discrete artificial boundary conditions are determined by the solution of the ODE. In general, it is local in time, but it is non-local in space. Several numerical examples are given to verify the superiority of the proposed method. |
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