The authors prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics,which serves as a powerful instrument in finding saddle points and constructing the solution la...The authors prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics,which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems on the high-dimensional sphere.Due to the semi-implicit treatment and the novel computational procedure,the orthonormality of numerical solutions at each time step could not be fully employed to simplify the derivations,and the computations of the state variable and directional vectors are coupled with the retraction,the vector transport and the orthonormalization procedure,which significantly complicates the analysis.They address these issues to prove error estimates for the proposed semi-implicit scheme and then carry out numerical experiments to substantiate the theoretical findings.展开更多
Numerical models with hydrostatic pressure have been widely utilized in studying flows in rivers, estuaries and coastal areas. The hydrostatic assumption is valid for the large-scale surface flows where the vertical a...Numerical models with hydrostatic pressure have been widely utilized in studying flows in rivers, estuaries and coastal areas. The hydrostatic assumption is valid for the large-scale surface flows where the vertical acceleration can be ignored, but for some particular cases the hydrodynamic pressure is important. In this paper, a vertical 2t） mathematical model with non-hydrostatic pressure was implemented in the σ coordinate. A fractional step method was used to enable the pressure to be decomposed into hydrostatic and hydrodynamic components and the predictor-corrector approach was applied to integration in time domain. Finally, several computational cases were studied to validate the importance of contributions of the hydrodynamic pressure.展开更多
Quantitative studies of scientific problems require solving correspondent mathematical models. Although a great deal of mathematical models of evolutional problems are set up under continuous space-time meaning, they ...Quantitative studies of scientific problems require solving correspondent mathematical models. Although a great deal of mathematical models of evolutional problems are set up under continuous space-time meaning, they usually had to be solved numerically after space-time discretization because nonlinear mathematical models except some展开更多
基金supported by the National Natural Science Foundation of China(Nos.12225102,12050002,12288101,12301555)the National Key R&D Program of China(No.2021YFF1200500)the Taishan Scholars Program of Shandong Province。
文摘The authors prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics,which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems on the high-dimensional sphere.Due to the semi-implicit treatment and the novel computational procedure,the orthonormality of numerical solutions at each time step could not be fully employed to simplify the derivations,and the computations of the state variable and directional vectors are coupled with the retraction,the vector transport and the orthonormalization procedure,which significantly complicates the analysis.They address these issues to prove error estimates for the proposed semi-implicit scheme and then carry out numerical experiments to substantiate the theoretical findings.
基金Project supported by the National Nature Science Foundation of China (Grant No :10172058) and Ministry of Education of China through the Ph.D. Program(Grant No :2000024817)
文摘Numerical models with hydrostatic pressure have been widely utilized in studying flows in rivers, estuaries and coastal areas. The hydrostatic assumption is valid for the large-scale surface flows where the vertical acceleration can be ignored, but for some particular cases the hydrodynamic pressure is important. In this paper, a vertical 2t） mathematical model with non-hydrostatic pressure was implemented in the σ coordinate. A fractional step method was used to enable the pressure to be decomposed into hydrostatic and hydrodynamic components and the predictor-corrector approach was applied to integration in time domain. Finally, several computational cases were studied to validate the importance of contributions of the hydrodynamic pressure.
文摘Quantitative studies of scientific problems require solving correspondent mathematical models. Although a great deal of mathematical models of evolutional problems are set up under continuous space-time meaning, they usually had to be solved numerically after space-time discretization because nonlinear mathematical models except some
