In this short paper,we remove the restrictionγ∈(1,3]that was used in the paper"The rate of convergence of the viscosity method for a nonlinear hyperbolic system"(Nonlinear Analysis,1999,38:435-445)and obta...In this short paper,we remove the restrictionγ∈(1,3]that was used in the paper"The rate of convergence of the viscosity method for a nonlinear hyperbolic system"(Nonlinear Analysis,1999,38:435-445)and obtain a global Holder continuous solution and the convergent rate of the viscosity method for the Cauchy problem of the variant nonisentropic system of polytropic gas for any adiabatic exponentγ>1.展开更多
In this paper,effective Eulerian algorithms are introduced for the computation of the forwardfinite time Lyapunov exponent(FTLE)of smoothflowfields.The advantages of the proposed algorithms mainly manifest in two aspe...In this paper,effective Eulerian algorithms are introduced for the computation of the forwardfinite time Lyapunov exponent(FTLE)of smoothflowfields.The advantages of the proposed algorithms mainly manifest in two aspects.First,previous Eulerian approaches for computing the FTLEfield are improved so that the Jacobian of theflow map can be obtained by directly solving a corresponding system of partial differential equations,rather than by implementing certainfinite difference upon theflow map,which can significantly improve the accuracy of the numerical solution especially near the FTLE ridges.Second,in the proposed algorithms,all computations are done on thefly,that is,all required partial differential equations are solved forward in time,which is practically more natural.The new algorithms still maintain the optimal computational complexity as well as the second order accuracy.Numerical examples demonstrate the effectiveness of the proposed algorithms.展开更多
By utilizing a novel quasi-harmonic three-layer dielectric model for the interface between a dielectric spheroid and the surrounding dissimilar dielectric medium,a robust numerical method for calculating the generaliz...By utilizing a novel quasi-harmonic three-layer dielectric model for the interface between a dielectric spheroid and the surrounding dissimilar dielectric medium,a robust numerical method for calculating the generalized Coulomb and self-polarization potentials of the dielectric spheroid is presented in this paper.The proposed numerical method can not only overcome the inherent mathematical divergence in the self-polarization energy which arises for the simplest step-like model of the dielectric interface,but also completely eliminate the potential numerical divergence which may occur in other treatments.Numerical experiments have demonstrated the convergence of the proposed numerical method as the number of the steps used to discretize the translation layer in a general three-layer dielectric model goes to infinity.展开更多
基金supported by the National Natural Science Foundation of China(12071409)。
文摘In this short paper,we remove the restrictionγ∈(1,3]that was used in the paper"The rate of convergence of the viscosity method for a nonlinear hyperbolic system"(Nonlinear Analysis,1999,38:435-445)and obtain a global Holder continuous solution and the convergent rate of the viscosity method for the Cauchy problem of the variant nonisentropic system of polytropic gas for any adiabatic exponentγ>1.
基金supported by the National Natural Science Foundation of China(12071409)the Natural Science Foundation of Jiangsu Province(BK20211293).
文摘In this paper,effective Eulerian algorithms are introduced for the computation of the forwardfinite time Lyapunov exponent(FTLE)of smoothflowfields.The advantages of the proposed algorithms mainly manifest in two aspects.First,previous Eulerian approaches for computing the FTLEfield are improved so that the Jacobian of theflow map can be obtained by directly solving a corresponding system of partial differential equations,rather than by implementing certainfinite difference upon theflow map,which can significantly improve the accuracy of the numerical solution especially near the FTLE ridges.Second,in the proposed algorithms,all computations are done on thefly,that is,all required partial differential equations are solved forward in time,which is practically more natural.The new algorithms still maintain the optimal computational complexity as well as the second order accuracy.Numerical examples demonstrate the effectiveness of the proposed algorithms.
基金the support of the National Natural Science Foundation of China(Grant No.10971181)the support of the National Institutes of Health(Grant No.1R01GM083600-03).
文摘By utilizing a novel quasi-harmonic three-layer dielectric model for the interface between a dielectric spheroid and the surrounding dissimilar dielectric medium,a robust numerical method for calculating the generalized Coulomb and self-polarization potentials of the dielectric spheroid is presented in this paper.The proposed numerical method can not only overcome the inherent mathematical divergence in the self-polarization energy which arises for the simplest step-like model of the dielectric interface,but also completely eliminate the potential numerical divergence which may occur in other treatments.Numerical experiments have demonstrated the convergence of the proposed numerical method as the number of the steps used to discretize the translation layer in a general three-layer dielectric model goes to infinity.
