Parallel Implementation of the Particle Finite Element Method - Second Generation

Abstract

Particle Finite Element Method - Second Generation (PFEM-2) is a numerical method written in a Lagrangian formulation that uses both particles and a mesh to solve the physics equations in an uncoupled way. The method uses fractional-steps with explicit and implicit calculations as needed.
The difference with the original form, is that in this second generation a temporal integration scheme based on streamlines integration is added while for the spatial discretization a point-colocation method is adopted. PFEM-2 has proved to obtain accurate and stable results, but it is necessary to make an efficient implementation to get a competitive code saving computing time.
Given that the particle based methods are inherently parallelizable, the present work is focused on the analysis, the comparison and the selection of the optimal tools and techniques to be used to solve, in an efficient way, each algorithm’s critical stages in each time steps. Those critical stages are the particle trajectory and acceleration computation through streamlines time integration, the remeshing and the equation system solver on the mesh (necessary for implicit calculations).
Finally, results obtained with this implementation are presented, allowing to simulate, with accuracy, robustness and at a reasonable computational cost, large numbers of particles in problems with scalar unknowns, such as scalar transport problems, and vectorials unknows, such as fluid-dynamic problems.