Study on Non-local Cubic Spline Function Based on Peridynamics

Cubic spline function is popular in modeling field because of its excellent properties, but it is difficult to solve because the derivative does not exist in discontinuity of displacement. And when the interpolation point is sparse, the interpolation curve isn’t good. Peridynamic is well in the problem of discontinuity. Therefore, the non-local operator is introduced by peridynamics and non-local calculus theory, and the interpolation method with first-order smoothness is provided. Then the concept of non-local mapping is introduced to the cubic spline interpolation function with second-order smoothness, and non-local cubic spline function and its numerical computational method are definited. This method not only preserves the smoothness of the spline function, but also achieves the good property of the non-local interpolation. It is more accurate and can better show the trend of the data points than the traditional cubic spline interpolation when the interpolation point is sparse.