Preserving physical properties such as positivity and mass is necessary for ensuring stability and accuracy in many scientific applications. For instance a negative density and may cause a numerical scheme to blow up. In this work, we investigate and develop different high-order polynomial approximations that preserve positivity and/or mass for mapping between different meshes.
We have developed an adaptive polynomial interpolation based on Newton polynomial that preserves positivity or data boundedness. This work uses the adaptive nature of the Newton polynomial to arrive at sufficient conditions for preserving the desired properties.
As we move to the next generation of supercomputer with complex integrated architectures, it is important to develop, and transform existing legacy codes to take advantage of the hardware resources for performance while maintaining portability. In this work, we investigate programming paradigms for advance optimization strategies for high performing and portable scientific software with primary focus to Numerical Weather Prediction (NWP) codes.
As a part of this project, We optimized different physics routines in NWP codes to better take advantage of Intel many- and multi-core architectures. We investigate the use of OpenMP API directives for vectorization of complex loops and outlined various code and data transformations required to enable thread and vector parallelism in NWP physics codes.
In this project, we investigated different search structures for Lagrangian based particle path tracing. Lagrangian basis particle path tracing seek to approximate the path (journey) of seeded particles given a set of Lagrangian basis flows. In order to reconstruct the paths one must identify the neighboring basis flows for each particle.
We investigated the use of traditional K-d trees and bounding volume hierarchy(BVH) trees as search structures in the context of Lagrangian based particle path tracing. We evaluated the storage size, the build time, and the search time of the different search structures over various configurations. The results from the studies can be found here [PDF].