ON WEIGHTED ORTHOGONAL BASIS FUNCTION IN MLS WITH MESHLESS LOCAL PETROV GALERKIN METHOD

The moving least square scheme is among the most successful schemes to generate meshfree shape functions in meshfree methods. It is computationally expensive due to computation of the inverse of the moment matrix. Recently, a weighted orthogonal basis function based moving least square approximation has been used in few meshfree methods such as element free Galerkin method, boundary element free method and global boundary node method. The moment matrix becomes diagonal matrix due to the orthogonal basis functions, and thus, the moment matrix becomes diagonal with trivial inverse. In the current work, weighted orthogonal basis functions based moving least square approximation is used in meshless local Petrov Galerkin method. We have tested this new method with the meshless local Petrov Galerkin method for one- and twodimensional Poisson equation. The numerical experiments have confirmed that the new approach provides the same accuracy and convergence rate but with higher computational efficiency than the classical moving least square with meshless local Petrov Galerkin method.