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The Multilevel Fast Multipole Algorithm (MLFMA) has known applications in scientific modeling in the fields of telecommunications, physics, mechanics, and chemistry. Accelerating calculation of far-field using GPUs and GPU clusters for large-scale problems has been studied for more than a decade. The acceleration of the Near Field Computation (P2P operator) however was less of a concern because it does not face the challenges of distributed processing which does far field. This article proposes a modification of the P2P algorithm and uses performance models to determine its optimality criteria. By modeling the speedup, we found that making threads independence by creating redundancy in the data makes the algorithm for lower dense (higher frequency) problems nearly 13 times faster than non-redundant mode.

In the present study, the ionic transport and selectivity of electrokinetically-driven flow of power-law fluids in a long pH-regulated rectangular nanochannel are analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. Non-linear Poisson-Boltzmann equation along with the association/dissociation reactions on the surface is considered. In addition, numerical simulations with the finite element method in 3D space are performed to compare the results with those obtained from 2D analysis. Moreover, an analytical solution under Debye-H\"uckel approximation for the limiting case of a slit nanochannel is derived and its results are compared with those obtained from numerical simulations. It is shown that the channel aspect ratio can influence all the physicochemical parameters. It is observed that the mean velocity and the convective ionic conductance are strong descending functions of the flow behavior index. By investigating the non-Newtonian fluid behavior effect, it is revealed that its impact on the ionic conductance becomes significant at high values of the solution pH and its variation can alter the anionic transport direction inside the nanochannel. Moreover, it is shown the flow behavior index can strongly influence the ion selectivity of the nanochannel and its variation can be used to let the selectivity go through its maximum as a function of pH., Comment: 51 pages, 14 figures