If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restric...If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restricted by the stability criterion in computational region. However, the excessively small time-step is usually unnecessary for a large portion of computational region. In this paper, a varying time-step explicit numerical integration algorithm is introduced, and its basic idea is to use different time-step restricted by the stability criterion in different computational region. Finally, the feasibility of the algorithm and its effect on calculating precision are verified by numerical test.展开更多
Viscoelastic artificial boundaries are widely adopted in numerical simulations of wave propagation problems.When explicit time-domain integration algorithms are used,the stability condition of the boundary domain is s...Viscoelastic artificial boundaries are widely adopted in numerical simulations of wave propagation problems.When explicit time-domain integration algorithms are used,the stability condition of the boundary domain is stricter than that of the internal region due to the influence of the damping and stiffness of an viscoelastic artificial boundary.The lack of a clear and practical stability criterion for this problem,however,affects the reasonable selection of an integral time step when using viscoelastic artificial boundaries.In this study,we investigate the stability conditions of explicit integration algorithms when using three-dimensional(3D)viscoelastic artificial boundaries through an analysis method based on a local subsystem.Several boundary subsystems that can represent localized characteristics of a complete numerical model are established,and their analytical stability conditions are derived from and further compared to one another.The stability of the complete model is controlled by the corner regions,and thus,the global stability criterion for the numerical model with viscoelastic artificial boundaries is obtained.Next,by analyzing the impact of different factors on stability conditions,we recommend a stability coefficient for practically estimating the maximum stable integral time step in the dynamic analysis when using 3D viscoelastic artificial boundaries.展开更多
基金National Natural Science Foundation of China (50178065), 973 Program (2002CB412706), National Social Com-monweal Research Foundation (2002DIB30076) and Joint Seismological Science Foundation (101066).
文摘If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restricted by the stability criterion in computational region. However, the excessively small time-step is usually unnecessary for a large portion of computational region. In this paper, a varying time-step explicit numerical integration algorithm is introduced, and its basic idea is to use different time-step restricted by the stability criterion in different computational region. Finally, the feasibility of the algorithm and its effect on calculating precision are verified by numerical test.
基金National Natural Science Foundation of China under Grant Nos.52108458 and U1839201China National Postdoctoral Program of Innovative Talents under Grant No.BX20200192+1 种基金Shuimu Tsinghua Scholar Program under Grant No.2020SM005National Key Research and Development Program of China under Grant No.2018YFC1504305。
文摘Viscoelastic artificial boundaries are widely adopted in numerical simulations of wave propagation problems.When explicit time-domain integration algorithms are used,the stability condition of the boundary domain is stricter than that of the internal region due to the influence of the damping and stiffness of an viscoelastic artificial boundary.The lack of a clear and practical stability criterion for this problem,however,affects the reasonable selection of an integral time step when using viscoelastic artificial boundaries.In this study,we investigate the stability conditions of explicit integration algorithms when using three-dimensional(3D)viscoelastic artificial boundaries through an analysis method based on a local subsystem.Several boundary subsystems that can represent localized characteristics of a complete numerical model are established,and their analytical stability conditions are derived from and further compared to one another.The stability of the complete model is controlled by the corner regions,and thus,the global stability criterion for the numerical model with viscoelastic artificial boundaries is obtained.Next,by analyzing the impact of different factors on stability conditions,we recommend a stability coefficient for practically estimating the maximum stable integral time step in the dynamic analysis when using 3D viscoelastic artificial boundaries.
