Collocated Mixed Discrete Least Squares Meshless (CMDLSM) method for solving quadratic partial differential equations

In this paper, a collocated Mixed Discrete Least Squares Meshless (MDLSM) method is proposed and used to attain an efficient solution to engineering problems. Background mesh is not required in the MDLSM method; hence, the method is a truly meshless method. Nodal points are used in the MDLSM methods to construct the shape functions, while collocated points are used to form the least squares functional. In the original MDLSM method, the locations of the nodal points and collocated points are the same. In the proposed Collocated Mixed Discrete Least Squares Meshless (CMDLSM) method, a set of additional collocated points is introduced. It is expected that the accuracy of results may improve by using the additional collocated points. It is noted that the size of coefficient matrix is not increased in the proposed CMDLSM method compared with the MDLSM method. Therefore, the required computational effort for solving the linear algebraic system of equations is same as that in MDLSM method. A set of benchmark numerical examples, cited in the literature, is used to evaluate the performance of the proposed method. The results indicate that the accuracy of solutions is improved by using additional collocated points in the proposed CMDLSM method. (C) 2018 Sharif University of Technology. All rights reserved.