A parallel iterative Finite Difference (FD) method for solving Poisson's equation on CUDA is implemented. The aim of this paper is to give a detail explanation about the parallel solution of a Partial Differential Equation (PDE). To examine the performance of the implemented iterative algorithm, a number of experiments were tested. The performance shows the benefit of using the implemented approach on GPU devices in terms of execution time.

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Atmospheric processes over the Mexican continental territory can be influenced by the occurrence of tropical cyclones (TCs) over the adjacent oceans.Furthermore, the Mexican territory is characterized by the presence of diurnal cycles of lightning. The Lightning Potential Index (LPI), that is a measure of the potential for charge generation and separation that leads to lightning production in convective storms, was assessed for the diurnal variability of lightning that exhibited a strong diurnal cycle over the Mexican continental territory when TC Bud was over the adjacent eastern Pacific Ocean. The assessment, from 0000 UTC 10 June to 2000 UTC 15 June 2018, used the Weather Research and Forecasting (WRF) model with a new hybrid terrainfollowing sigma-pressure vertical coordinate. Two ensembles with various cumulus and microphysical parameterizations were performed with a grid spacing of 2 km. In one ensemble, sea surface temperature (SST) was prescribed from the Real-time global (RTG) SST analysis product and allowed to evolve interactively with the modeled atmosphere. Then, all the ensemble members were compared against available observations from the World Wide Lightning Location Network (WWLLN) to evaluate which model configurations perform best. It is not known if the LPI is capable of reproducing diurnal cycles of lightning over tropical regions; and the results allow gaining an understanding of the LPI when it reproduces the observed diurnal variability of lightning over land. The ensemble members that had better performances were those that included the prescribed SST.