Final Report for project: Domain decomposition, load balancing, and massively parallel solvers for the class of nonlocal models
By: Pranav Gadikar
Mentors: Patrick Diehl, Prashant K. Jha
Project Proposal
Description of the problem
Recently various nonlocal models have been proposed and applied for understanding of complex spatially multiscale phenomena in diverse fields such as solid mechanics, fluid mechanics, particulate media, directed self-assembly of Block-Copolymer, tumor modeling, etc. Unlike local models which are governed by partial differential equations such as heat equation, wave equation, nonlocal models have dependence over a larger length than the size of discretization. This makes the partitioning of mesh and information sharing among the processors more difficult. Also, the amount of data communicated among the processors is higher compared to what is expected in the local models. The challenge is also to not have idle processors during the communication step. It is our understanding that an efficient computational method to solve the nonlocal model is very important and will have impact in many fields. The algorithm developed for one field can be easily applied and extended to models in the other fields. Our main goal in this project is to highlight and address the key difficulties in designing massively parallel schemes for nonlocal models while keeping the model related complexity to minimum. To meet the previous goal and to fix the ideas, we use the nonlocal heat equation in 2D setting. We utilize a modern parallelization library, HPX, to develop the parallel solver.
