In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approxima...In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations （ODEs）. Then, the converted ODE system is solved by the exponential time difference （ETD） method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.展开更多
In this article,we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers’equation in rectangu-lar coordinates.The convergence analys...In this article,we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers’equation in rectangu-lar coordinates.The convergence analysis for the new iteration method is discussed in details.We compared the results of Burgers’equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.展开更多
文摘In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations （ODEs）. Then, the converted ODE system is solved by the exponential time difference （ETD） method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.
基金supported by"The Council of Scientific and Industrial Research"under research Grant No.09/045(0836)2009-EMR-I.
文摘In this article,we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers’equation in rectangu-lar coordinates.The convergence analysis for the new iteration method is discussed in details.We compared the results of Burgers’equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.
