A class of cubic trigonometric interpolation spline curves with two parameters is presented in this paper. The spline curves can automatically interpolate the given data points and become C^2 interpolation curves with...A class of cubic trigonometric interpolation spline curves with two parameters is presented in this paper. The spline curves can automatically interpolate the given data points and become C^2 interpolation curves without solving equations system even if the interpolation conditions are fixed. Moreover, shape of the interpolation spline curves can be globally adjusted by the two parameters. By selecting proper values of the two parameters,the optimal interpolation spline curves can be obtained.展开更多
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （...Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.展开更多
General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation a...General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation and barycentric rational Her- mite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.展开更多
Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity proble...Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares （IMLS） method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin （IEFG） method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method.展开更多
基金supported by the National Natural Science Foundation of China(11171181)the Scientific Research Fund of Hunan Provincial Education Department of China(14B099)
文摘A class of cubic trigonometric interpolation spline curves with two parameters is presented in this paper. The spline curves can automatically interpolate the given data points and become C^2 interpolation curves without solving equations system even if the interpolation conditions are fixed. Moreover, shape of the interpolation spline curves can be globally adjusted by the two parameters. By selecting proper values of the two parameters,the optimal interpolation spline curves can be obtained.
基金financially supported by the National Natural Science Foundation of China(11202081,11272124,and 11472109)the State Key Lab of Subtropical Building Science,South China University of Technology(2014ZC17)
文摘Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
基金supported by the grant of Key Scientific Research Foundation of Education Department of Anhui Province, No. KJ2014A210
文摘General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation and barycentric rational Her- mite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171208)the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)
文摘Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares （IMLS） method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin （IEFG） method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method.
