Accurate forecasts have a direct impact on how we prepare at personal, regional, and global levels for different weather events. Many of the current numerical weather prediction (NWP) systems use legacy codes that are not adequately designed to take advantage of current and future modern compute resources. As we prepare for the Exascale era and the next generation of weather forecast systems, the ability of theses codes to efficiently use the computational resources is paramount for meeting the time requirement of forecasting and the desired resolution of 1 km. Many of the NWP codes are multidisciplinary in nature, combining building blocks from various areas of physics and atmospheric sciences. This introduces the challenge of stitching these building blocks together. For example, some NWP systems use different meshes for the dynamics and the physics. This difference introduces negative and nonphysical quantities when mapping between physics and dynamics meshes. In this context, a mapping that does not preserve positivity leads to unstable simulation and a positive bias in the prediction of quantities such as moisture. This research focuses on 1) investigating different approaches for accelerating the physics schemes in NWP codes; and 2) developing a high-order positivity-preserving method (https://github.com/ouermijudicael/HiPPIS) for mapping solution values between different meshes.