Parallel EFG algorithm for heat transfer problems

At present, meshless element free Galerkin (EFG) method is being successfully applied in the areas such as solid mechanics, fracture mechanics and thermal. Being a meshless method, it has many advantages over finite element method. One big hurdle with the wide implementation of this method is its computational cost. Therefore, in this paper, a parallel algorithm is proposed for the EFG method. The parallel code has been written in FORTRAN language using MPI message passing library and executed on a four node (eight processors) MIMD type, distributed memory 'PARAM 10000' parallel computer. The total time, communication time, speedup and efficiency have been estimated for a three-dimensional heat transfer problem to validate the proposed algorithm. For eight processors, the speedup and efficiency are obtained to be 4.66 and 58.22%, respectively, for a data size of 1320 nodes.