In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, th...In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.展开更多
The three-dimensional numerical manifold method(3DNMM) method is further enriched to simulate wave propagation across homogeneous/jointed rock masses. For the purpose of minimizing negative effects from artificial bou...The three-dimensional numerical manifold method(3DNMM) method is further enriched to simulate wave propagation across homogeneous/jointed rock masses. For the purpose of minimizing negative effects from artificial boundaries, a viscous nonreflecting boundary, which can effectively absorb the energy of a wave, is firstly adopted to enrich 3DNMM. Then, to simulate the elastic recovery property of an infinite problem domain, a viscoelastic boundary, which is developed from the viscous nonreflecting boundary, is further adopted to enrich 3DNMM. Finally, to eliminate the noise caused by scattered waves, a force input method which can input the incident wave correctly is incorporated into 3DNMM. Five typical numerical tests on P/S-wave propagation across jointed/homogeneous rock masses are conducted to validate the enriched 3DNMM. Numerical results indicate that wave propagation problems within homogeneous and jointed rock masses can be correctly and reliably modeled with the enriched 3DNMM.展开更多
The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge memory consumption of the gradient preconditioning algorithms based on the Hessian matrix. However, the accuracy of thi...The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge memory consumption of the gradient preconditioning algorithms based on the Hessian matrix. However, the accuracy of this approach is prone to be influ- enced by the energy of reflected waves. To tackle this problem, the paper proposes a new gradient preconditioning method based on the energy of transmitted waves. The approach scales the gradient through a precondition factor, which is calculated by the ‘ap- proximate transmission wavefield’ simulation based on the nonreflecting acoustic wave equation. The method requires no computing nor storing of the Hessian matrix and its inverse matrix. Furthermore, the proposed method can effectively eliminate the effects of geometric spreading and disproportionality in the gradient illumination. The results of model experiments show that the time-domain full waveform inversion (FWI) using the gradient preconditioning based on transmitted wave energy can achieve higher inversion accuracy for deep high-velocity bodies and their underlying strata in comparison with the one using the gradient preconditioning based on seismic wave energy. The field marine seismic data test shows that our proposed method is also highly applicable to the FWI of field marine seismic data.展开更多
In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are pr...In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are proposed as a substitute of the nonreflecting boundary conditions inside boundary layers near rigid walls. These derived boundary conditions are then applied to calculations both for the Euler equations and the Navier-Stokes equations to determine if they can produce acceptable results for the subsonic flows in channels. The numerical results obtained by an implicit second-order upwind difference scheme show the effective- ness and generality of the boundary conditions. Furthermore, the formulae and the analysis performed here may be extended to three dimensional problems.展开更多
Time-dependent fractional partial differential equations typically require huge amounts of memory and computational time,especially for long-time integration,which taxes computational resources heavily for high-dimens...Time-dependent fractional partial differential equations typically require huge amounts of memory and computational time,especially for long-time integration,which taxes computational resources heavily for high-dimensional problems.Here,we first analyze existing numerical methods of sum-of-exponentials for approximating the kernel function in constant-order fractional operators,and identify the current pitfalls of such methods.In order to overcome the pitfalls,an improved sum-of-exponentials is developed and verified.We also present several sumof-exponentials for the approximation of the kernel function in variable-order fractional operators.Subsequently,based on the sum-of-exponentials,we propose a unified framework for fast time-stepping methods for fractional integral and derivative operators of constant and variable orders.We test the fast method based on several benchmark problems,including fractional initial value problems,the time-fractional Allen-Cahn equation in two and three spatial dimensions,and the Schr¨odinger equation with nonreflecting boundary conditions,demonstrating the efficiency and robustness of the proposed method.The results show that the present fast method significantly reduces the storage and computational cost especially for long-time integration problems.展开更多
Transparent boundary conditions(TBCs)for anisotropic vertical transverse isotropic VTI medium are formulated for the axially symmetric case.The high accuracy of the derived TBCs and their long-time stability are demon...Transparent boundary conditions(TBCs)for anisotropic vertical transverse isotropic VTI medium are formulated for the axially symmetric case.The high accuracy of the derived TBCs and their long-time stability are demonstrated in numerical experiments.The TBCs are represented in terms of the vertical component of the velocity vector and tangential component of the stress tensor that facilitates the easy implementation of the boundary condition into the finite-difference staggered-grid scheme.展开更多
基金This work is supported partly by the Special Funds for Major State Basic Research Projects of China and the National Science Foundation of China.
文摘In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.
基金supported by the Youth Innovation Promotion Association CAS(Grant No. 2020327)the National Natural Science Foundation of China(Grant Nos. 12202024, 52130905, 12272393, and 12072357)。
文摘The three-dimensional numerical manifold method(3DNMM) method is further enriched to simulate wave propagation across homogeneous/jointed rock masses. For the purpose of minimizing negative effects from artificial boundaries, a viscous nonreflecting boundary, which can effectively absorb the energy of a wave, is firstly adopted to enrich 3DNMM. Then, to simulate the elastic recovery property of an infinite problem domain, a viscoelastic boundary, which is developed from the viscous nonreflecting boundary, is further adopted to enrich 3DNMM. Finally, to eliminate the noise caused by scattered waves, a force input method which can input the incident wave correctly is incorporated into 3DNMM. Five typical numerical tests on P/S-wave propagation across jointed/homogeneous rock masses are conducted to validate the enriched 3DNMM. Numerical results indicate that wave propagation problems within homogeneous and jointed rock masses can be correctly and reliably modeled with the enriched 3DNMM.
基金support of the NSFCShandong Joint Fund for Marine Science Research Centers (No. U1606401)the National Natural Science Foundation of China (Nos. 41574105 and 41704114)+1 种基金the National Science and Technology Major Project of China (No.2016ZX05027-002)Taishan Scholar Project Funding (No. tspd20161007)
文摘The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge memory consumption of the gradient preconditioning algorithms based on the Hessian matrix. However, the accuracy of this approach is prone to be influ- enced by the energy of reflected waves. To tackle this problem, the paper proposes a new gradient preconditioning method based on the energy of transmitted waves. The approach scales the gradient through a precondition factor, which is calculated by the ‘ap- proximate transmission wavefield’ simulation based on the nonreflecting acoustic wave equation. The method requires no computing nor storing of the Hessian matrix and its inverse matrix. Furthermore, the proposed method can effectively eliminate the effects of geometric spreading and disproportionality in the gradient illumination. The results of model experiments show that the time-domain full waveform inversion (FWI) using the gradient preconditioning based on transmitted wave energy can achieve higher inversion accuracy for deep high-velocity bodies and their underlying strata in comparison with the one using the gradient preconditioning based on seismic wave energy. The field marine seismic data test shows that our proposed method is also highly applicable to the FWI of field marine seismic data.
文摘In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are proposed as a substitute of the nonreflecting boundary conditions inside boundary layers near rigid walls. These derived boundary conditions are then applied to calculations both for the Euler equations and the Navier-Stokes equations to determine if they can produce acceptable results for the subsonic flows in channels. The numerical results obtained by an implicit second-order upwind difference scheme show the effective- ness and generality of the boundary conditions. Furthermore, the formulae and the analysis performed here may be extended to three dimensional problems.
基金supported by the NSF of China(Nos.12171283,12071301,12120101001)the National Key R&D Program of China(2021YFA1000202)+2 种基金the startup fund from Shandong University(No.11140082063130)the Shanghai Municipal Science and Technology Commission(No.20JC1412500)the science challenge project(No.TZ2018001).
文摘Time-dependent fractional partial differential equations typically require huge amounts of memory and computational time,especially for long-time integration,which taxes computational resources heavily for high-dimensional problems.Here,we first analyze existing numerical methods of sum-of-exponentials for approximating the kernel function in constant-order fractional operators,and identify the current pitfalls of such methods.In order to overcome the pitfalls,an improved sum-of-exponentials is developed and verified.We also present several sumof-exponentials for the approximation of the kernel function in variable-order fractional operators.Subsequently,based on the sum-of-exponentials,we propose a unified framework for fast time-stepping methods for fractional integral and derivative operators of constant and variable orders.We test the fast method based on several benchmark problems,including fractional initial value problems,the time-fractional Allen-Cahn equation in two and three spatial dimensions,and the Schr¨odinger equation with nonreflecting boundary conditions,demonstrating the efficiency and robustness of the proposed method.The results show that the present fast method significantly reduces the storage and computational cost especially for long-time integration problems.
文摘Transparent boundary conditions(TBCs)for anisotropic vertical transverse isotropic VTI medium are formulated for the axially symmetric case.The high accuracy of the derived TBCs and their long-time stability are demonstrated in numerical experiments.The TBCs are represented in terms of the vertical component of the velocity vector and tangential component of the stress tensor that facilitates the easy implementation of the boundary condition into the finite-difference staggered-grid scheme.
