Amirkabir University of TechnologyAmirkabir Journal of Civil Engineering2588-297X51420191023Mapped Moving Least Squares Approximation Used in Mixed Discrete Least Squares Meshfree MethodMapped Moving Least Squares Approximation Used in Mixed Discrete Least Squares Meshfree Method805816301810.22060/ceej.2018.13861.5505FAMortezaKolahdoozanEhsanAmaniDepartment of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IranSaebFarajiDepartment of Civil and Environmental Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IranJournal Article20180102The Mixed Least Squares Meshfree (MDLSM) method has shown its appropriate efficiency for solving Partial Differential Equations (PDEs) related to the engineering problems. The method is based on the minimizing the residual functional. The residual functional is defined as a summation of the weighted residuals on the governing PDEs and the boundaries. The Moving Least Squares (MLS) is usually applied in the MDLSM method for constructing the shape functions. Although the required consistency and compatibility for the approximation function are satisfied by the MLS, the method loses its appropriate efficiency when the nodal points cluster become too much. In the current study, the mentioned drawback is overcome using the novel approximation function called Mapped Moving Least Squares (MMLS). In this approach, the cluster of closed nodal was pointed maps to standard nodal distribution. Then the approximation function and its derivatives were computed incorporating some consideration. The efficiency of suggested MMLS for overcoming the drawback of MLS was evaluated by approximating the mathematical function. The obtained results showed the ability of suggested MMLS method to solve the drawback. The suggested approximation function was applied in MDLSM method, and used for solving the Burgers equations. Obtained results approved the efficiency of suggested method.The Mixed Least Squares Meshfree (MDLSM) method has shown its appropriate efficiency for solving Partial Differential Equations (PDEs) related to the engineering problems. The method is based on the minimizing the residual functional. The residual functional is defined as a summation of the weighted residuals on the governing PDEs and the boundaries. The Moving Least Squares (MLS) is usually applied in the MDLSM method for constructing the shape functions. Although the required consistency and compatibility for the approximation function are satisfied by the MLS, the method loses its appropriate efficiency when the nodal points cluster become too much. In the current study, the mentioned drawback is overcome using the novel approximation function called Mapped Moving Least Squares (MMLS). In this approach, the cluster of closed nodal was pointed maps to standard nodal distribution. Then the approximation function and its derivatives were computed incorporating some consideration. The efficiency of suggested MMLS for overcoming the drawback of MLS was evaluated by approximating the mathematical function. The obtained results showed the ability of suggested MMLS method to solve the drawback. The suggested approximation function was applied in MDLSM method, and used for solving the Burgers equations. Obtained results approved the efficiency of suggested method.https://ceej.aut.ac.ir/article_3018_ee45eb8b3e1064f8e1d86fc332a70338.pdf