A fully discrete Jacobi-spherical harmonic spectral method is provided for the Navier-Stokes equations in a ball. Its stability and convergence are proved. Numerical results show efficiency of this approach. The propo...A fully discrete Jacobi-spherical harmonic spectral method is provided for the Navier-Stokes equations in a ball. Its stability and convergence are proved. Numerical results show efficiency of this approach. The proposed method is also applicable to other problems in spherical geometry.展开更多
A pseudospectral method with symplectic algorithm for the solution of time-dependent Schrodinger equations （TDSE） is introduced. The spatial part of the wavefunction is discretized into sparse grid by pseudospectral...A pseudospectral method with symplectic algorithm for the solution of time-dependent Schrodinger equations （TDSE） is introduced. The spatial part of the wavefunction is discretized into sparse grid by pseudospectral method and the time evolution is given in symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSE. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atom in strong laser field as compared with previously published work. The influence of the additional static electric field is also investigated.展开更多
We present an efficient and realizable scheme for the generation of an ultrashort single attosecond（as） pulse from H atom with a 800-nm fundamental laser field combined with a terahertz（THz） field. The high-order ...We present an efficient and realizable scheme for the generation of an ultrashort single attosecond（as） pulse from H atom with a 800-nm fundamental laser field combined with a terahertz（THz） field. The high-order harmonic generation（HHG） can be obtained by solving the time-dependent Schr dinger equation accurately and efficiently with time-dependent generalized pseudo-spectral（TDGPS） method. The result shows that the plateau of high-order harmonics is extended and the broadband spectra can be produced by the combined laser pulse, which can be explained by the corresponding ionization probability. The time–frequency analysis and semi-classical three-step model are also presented to further investigate this mechanism. Besides, by the superposition of the harmonics near the cutoff region, an isolated 133-as pulse can be obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10771142)Science and Technology Commission of Shanghai Municipality(No.75105118)+2 种基金Shanghai Leading Academic Discipline Projects(Nos.T0401 and J50101)Fund for E-institutes of Universities in Shanghai(No.E03004)and Innovative Foundation of Shanghai University(No.A.10-0101-07-408)
文摘A fully discrete Jacobi-spherical harmonic spectral method is provided for the Navier-Stokes equations in a ball. Its stability and convergence are proved. Numerical results show efficiency of this approach. The proposed method is also applicable to other problems in spherical geometry.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10374119 and 10674154）, and The 0ne- Hundred-Talents Project of Chinese Academy of Science.Acknowledgments We gratefully acknowledge Professor Ding P Z and Professor Liu X S for their hospitality and help in symplectic algorithm.
文摘A pseudospectral method with symplectic algorithm for the solution of time-dependent Schrodinger equations （TDSE） is introduced. The spatial part of the wavefunction is discretized into sparse grid by pseudospectral method and the time evolution is given in symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSE. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atom in strong laser field as compared with previously published work. The influence of the additional static electric field is also investigated.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11174108,11104108,and 11271158)
文摘We present an efficient and realizable scheme for the generation of an ultrashort single attosecond（as） pulse from H atom with a 800-nm fundamental laser field combined with a terahertz（THz） field. The high-order harmonic generation（HHG） can be obtained by solving the time-dependent Schr dinger equation accurately and efficiently with time-dependent generalized pseudo-spectral（TDGPS） method. The result shows that the plateau of high-order harmonics is extended and the broadband spectra can be produced by the combined laser pulse, which can be explained by the corresponding ionization probability. The time–frequency analysis and semi-classical three-step model are also presented to further investigate this mechanism. Besides, by the superposition of the harmonics near the cutoff region, an isolated 133-as pulse can be obtained.
