An Efficient Hybrid Implementation of MLPG Method

Abstract

The computational implementation of moving least squares (MLS) shape functions is an important step to consider in some versions of the meshless local Petrov–Galerkin (MLPG) method for a variety of two-dimensional engineering problems. Here, the usage of conventional Gaussian quadrature in the MLPG may require an excessive number integration points to achieve acceptable accuracy. In addition, since for each integration point a search for nearby points contributing to the construction of the MLS shape functions is required, considerable increase in computational cost is often observed. Herein, an efficient hybrid implementation of CPU and GPU is proposed to accelerate the construction of MLS shape functions for MLPG. To this end, a new K-d-Tree (K-dimensional tree)-based data structure is introduced in order to accelerate the calculations involving computational geometry formulas such as MLS. The results are compared for implementations in CPU and [Formula: see text] using K-d-Tree with the traditional algorithm of brute force search of the neighboring points when dealing with two-dimensional linear elasticity problems. Finally, the performance gain in the numerical approximation is obtained when using the highlighted K-d-Tree.