In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been use...In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been used for this purpose.Traditional particle interpolation (TPI) is simple and easy to do, but its low accuracy has become an obstacle to its wider application.This can be seen in the cases of particle disorder arrangements and derivative calculations.There are many different methods to improve accuracy, with the moving least square (MLS) method one of the most important meshless interpolation methods.Unfortunately, it requires complex matrix computing and so is quite time-consuming.The authors developed a simpler scheme, called higher-order particle interpolation (HPI).This scheme can get more accurate derivatives than the MLS method, and its function value and derivatives can be obtained simultaneously.Although this scheme was developed for the SPH method, it has been found useful for other meshless methods.展开更多
For a Jordan domain D in the complex plane satisfying certain boundary conditions a function f B(D), we prove that the corresponding higher order Fejer interpolation polynomials based on Fejer points converge to f(z...For a Jordan domain D in the complex plane satisfying certain boundary conditions a function f B(D), we prove that the corresponding higher order Fejer interpolation polynomials based on Fejer points converge to f(z) uniformly on D. These extend some known results.展开更多
In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2...In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10572041,50779008Doctoral Fund of Ministry of Education of China under Grant No.20060217009
文摘In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been used for this purpose.Traditional particle interpolation (TPI) is simple and easy to do, but its low accuracy has become an obstacle to its wider application.This can be seen in the cases of particle disorder arrangements and derivative calculations.There are many different methods to improve accuracy, with the moving least square (MLS) method one of the most important meshless interpolation methods.Unfortunately, it requires complex matrix computing and so is quite time-consuming.The authors developed a simpler scheme, called higher-order particle interpolation (HPI).This scheme can get more accurate derivatives than the MLS method, and its function value and derivatives can be obtained simultaneously.Although this scheme was developed for the SPH method, it has been found useful for other meshless methods.
文摘For a Jordan domain D in the complex plane satisfying certain boundary conditions a function f B(D), we prove that the corresponding higher order Fejer interpolation polynomials based on Fejer points converge to f(z) uniformly on D. These extend some known results.
文摘In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.
