Adaptive Meshfree Methods Using Local Nodes and Radial Basis Functions

In this paper, adaptive meshfree methods using local nodes and radial basis functions (RBFs) which based on strong-form formulation is presented. In this present formulation, radial basis functions are used in the function approximation for the discretization of the governing system equations. Regularization techniques are suggested and examined to stabilize the solutions in order to obtain stable and accurate results. Different schemes for constructing regularization matrix are compared and discussed. As stability is restored, meshfree strong-form method using local nodes and RBFs can facilitate an easier implementation for adaptive analysis to achieve desired accuracy. Residual based error indicator is devised in the adaptive scheme. A simple and practical node refinement procedure is presented for node insertion at each adaptive step.

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