SUPERCONVERGENT SMOOTHED REPRODUCING GRADIENT MESHFREE COLLOCATION METHOD

The meshfree collocation (MC) method is straightforward to implement, but the computation efficiency is limited by the calculation of high order gradients of shape functions. In order to enhance the computation efficiency and convergence rate of the meshfree collocation method, this work proposes a superconvergent smoothed reproducing gradient meshfree collocation (SRGMC) method through combining meshfree gradient reproducing theory with gradient smoothing operations. In the proposed method, the first order reproduced gradients of meshfree shape functions are utilizing to iteratively construct the second order smoothed reproducing gradients, which further avoids the direct differentiation of the inverse matrix of the moment matrix in the shape functions. Furthermore, the present formulation is more concise and significantly improves computational efficiency. Numerical examples well demonstrate the accuracy and convergence of the presented SRGMC method, which is significantly superior to MC method.