Department of communication systems, Jozef Stefan Institute, Slovenia
Abhishek Kumar Singh
Department of Mechanical and Industrial Engineering, IIT Roorkee
Krishna Mohan Singh
Department of Mechanical and Industrial Engineering Indian Institute of Technology, Roorkee, 247667, India
In this paper, we propose meshless local Petrov Galerkin method based on stabilised moving least-squares approximation. Standard moving least squares (MLS) approximation is unstable at higher grid resolutions. Reason of this instability is ill-conditioning of moment matrix in the MLS procedure. As an evaluation point moves away from the origin, the condition number of the moment matrix increases. Further, the condition number also increases with the decrement of grid size. In the current work, we presented performance of the stabilised MLS approximation in the MLPG method for heat conduction problem and found that it provides stability at higher grid resolution.