This project aims to decrease improve weather forecasting through to use of high performance computing(HPC) to solve partial differential equations(PDEs). There are several examples of PDEs associated with weather forecasting, the calculations for which slow the prediction times and pose as an obstacle for aircraft and flight, costing time and money. The use of HPC to solve these PDEs would increase the efficiency of weather forecasting, making for safer air travel, as well as saving time and money. Examples of specific PDEs that affect weather forecasting that we aim to solve with HPC are: the Wave Equation, Heat or Diffusion Equation, Laplace\u27s Equation, Helmholtz Equation, Poisson\u27s Equation, Time-Independent Schrodinger Equation, and the Klein-Gordan Equation. Beginning with the Heat Equation, we will check the performance of HPC, comparing it to the performance of current weather forecasting calculations. We have chosen this PDE as it finds its applications in many scientific fields, including but not limited to weather prediction. Micah D. Schuster, a Computer Science professor at the Wentworth Institute of Technology, solved the heat equation by deriving the numerical scheme and then parallelizing the algorithm using OpenMP. The HPC performance was assessed by varying different parameters including the array size, block size, share, and hardware. Noting the success of this case study, we will be using these parameters to test the HPC of other PDEs and noting how this affects the time of weather prediction. To measure our results, we will include details about the performance metrics, identify any trade-offs for using HPC, HPC performance such as time and space
