To overcome the deficiencies of conventional geosynthetic-reinforced and pile-supported (GRPS) embankment, a new improvement technique, fixed geosynthetic technique of GRPS embankment (FGT embankment), was developed a...To overcome the deficiencies of conventional geosynthetic-reinforced and pile-supported (GRPS) embankment, a new improvement technique, fixed geosynthetic technique of GRPS embankment (FGT embankment), was developed and introduced. Based on the discussion about the load transfer mechanism of FGT embankment, a simplified check method of the requirement of geosynthetic tensile strength and a mechanical model of the FGT embankment were proposed. Two conditions, the pile cap and pile beam conditions are considered in the mechanical model. The finite difference method is used to solve the mechanical model owing to the complexity of the differential equations and the soil strata. Then, the numerical procedure is programmed. Finally, a field test is conducted to verify the mechanical model and the calculated results are in good agreement with field measured data.展开更多
Elastic waves in the seabed generated by low-frequency noise radiating from ships are known as ship seismic waves and can be used to detect and identify ships. To obtain the propagation characteristics of ship seismic...Elastic waves in the seabed generated by low-frequency noise radiating from ships are known as ship seismic waves and can be used to detect and identify ships. To obtain the propagation characteristics of ship seismic waves, an algorithm for calculating Seismic waves at the seafloor is presented based on the staggered-grid finite difference method. The accuracy of the algorithm was tested by comparison with analytical solutions. Numerical simulation of seismic waves generated by a low-frequency point sotmd source in a typical shallow sea environment was carried out. Using various source frequencies and locations in the numerical simulation, we show that the seismic waves in the near field are composed mostly of transmitted S-waves and interface waves while transmitted P-waves are weak near the seafloor. However, in the far field, the wave components of the seismic wave are mainly normal modes and interface waves, with the latter being relatively strong in the waveforms, As the source frequency decreases, the normal modes become smaller and the interface waves dominate the time series of the seismic waves.展开更多
We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation （NLDE） in the nonrelativistic limit regime, involving a small dimensionless parameter 0...We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation （NLDE） in the nonrelativistic limit regime, involving a small dimensionless parameter 0 〈 ε〈〈1 which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e., there are propagating waves with wavelength O（ ε^2） and O（1） in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference （CNFD） method and establish rigorously its error estimate which depends explicitly on the mesh size h and time step τ- as well as the small parameter 0 〈 ε≤1 Based on the error bound, in order to obtain ＇correct＇ numerical solutions in the nonrelativistic limit regime, i.e., 0 〈 ε≤1 , the CNFD method requests the ε-scalability： τ- = O（ε3） and h = O（√ε）. Then we propose and analyze two numerical methods for the discretization of NLDE by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time- splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their ε-scalability is improved to τ = O（ε2） and h = O（1） when 0 〈 ε 〈〈 1. Extensive numerical results are reported to confirm our error estimates.展开更多
This work is concerned with time stepping finite element methods for abstract second order evolution problems. We derive optimal order a posteriori error estimates and a posteriori nodal superconvergence error estimat...This work is concerned with time stepping finite element methods for abstract second order evolution problems. We derive optimal order a posteriori error estimates and a posteriori nodal superconvergence error estimates using the energy approach and the duality argument. With the help of the a posteriori error estimator developed in this work, we will further propose an adaptive time stepping strategy. A number of numerical experiments are performed to illustrate the reliability and efficiency of the a posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.展开更多
基金Project(51278216) supported by the National Natural Science Foundation of ChinaProject(20091341) supported by the Scientific Research Foundation for Returned Overseas Chinese Scholars,Ministry of Education,ChinaProject(HF-08-01-2011-240) supported by the Graduates’ Innovation Fund of Huazhong University of Science and Technology,China
文摘To overcome the deficiencies of conventional geosynthetic-reinforced and pile-supported (GRPS) embankment, a new improvement technique, fixed geosynthetic technique of GRPS embankment (FGT embankment), was developed and introduced. Based on the discussion about the load transfer mechanism of FGT embankment, a simplified check method of the requirement of geosynthetic tensile strength and a mechanical model of the FGT embankment were proposed. Two conditions, the pile cap and pile beam conditions are considered in the mechanical model. The finite difference method is used to solve the mechanical model owing to the complexity of the differential equations and the soil strata. Then, the numerical procedure is programmed. Finally, a field test is conducted to verify the mechanical model and the calculated results are in good agreement with field measured data.
基金Supported by the National Natural Science Foundation of China(Nos.51179195,51679248)the National Defense Foundation of China(No.513030203-02)
文摘Elastic waves in the seabed generated by low-frequency noise radiating from ships are known as ship seismic waves and can be used to detect and identify ships. To obtain the propagation characteristics of ship seismic waves, an algorithm for calculating Seismic waves at the seafloor is presented based on the staggered-grid finite difference method. The accuracy of the algorithm was tested by comparison with analytical solutions. Numerical simulation of seismic waves generated by a low-frequency point sotmd source in a typical shallow sea environment was carried out. Using various source frequencies and locations in the numerical simulation, we show that the seismic waves in the near field are composed mostly of transmitted S-waves and interface waves while transmitted P-waves are weak near the seafloor. However, in the far field, the wave components of the seismic wave are mainly normal modes and interface waves, with the latter being relatively strong in the waveforms, As the source frequency decreases, the normal modes become smaller and the interface waves dominate the time series of the seismic waves.
基金supported by the Ministry of Education of Singapore(Grant No.R146-000-196-112)National Natural Science Foundation of China(Grant No.91430103)
文摘We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation （NLDE） in the nonrelativistic limit regime, involving a small dimensionless parameter 0 〈 ε〈〈1 which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e., there are propagating waves with wavelength O（ ε^2） and O（1） in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference （CNFD） method and establish rigorously its error estimate which depends explicitly on the mesh size h and time step τ- as well as the small parameter 0 〈 ε≤1 Based on the error bound, in order to obtain ＇correct＇ numerical solutions in the nonrelativistic limit regime, i.e., 0 〈 ε≤1 , the CNFD method requests the ε-scalability： τ- = O（ε3） and h = O（√ε）. Then we propose and analyze two numerical methods for the discretization of NLDE by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time- splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their ε-scalability is improved to τ = O（ε2） and h = O（1） when 0 〈 ε 〈〈 1. Extensive numerical results are reported to confirm our error estimates.
基金supported by National Natural Science Foundation of China(Grant Nos.1117121911161130004 and 11101199)+1 种基金E-Institutes of Shanghai Municipal Education Commission(Grant No.E03004)Program for New Century Excellent Talents in Fujian Province University(Grant No.JA12260)
文摘This work is concerned with time stepping finite element methods for abstract second order evolution problems. We derive optimal order a posteriori error estimates and a posteriori nodal superconvergence error estimates using the energy approach and the duality argument. With the help of the a posteriori error estimator developed in this work, we will further propose an adaptive time stepping strategy. A number of numerical experiments are performed to illustrate the reliability and efficiency of the a posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.
