Integrated data management and dynamic load balancing for hp and generalized FEM

This dissertation discusses new schemes for data management and dynamic load balancing for parallel versions of hp and generalized finite element methods (GFEM). Parallel hp and GFEM promise to attain unprecedented levels of numerical accuracy and computation efficiencies leading to truly realistic computer simulations. However, the intrinsically dynamic and highly irregular patterns of data access, storage and load balancing make the implementations of these schemes difficult. Simple, efficient and integrated dynamic data management and load balancing schemes are developed in this study to resolve these difficulties.; The design of our dynamic data management and load balancing schemes starts with separating FEM data into persistent mesh data (PMD) and transient computational data (TCD). Such separation reduces FEM data management to PMD management using an “owner-computes” rule. To efficiently utilize the hierarchical memory structures in modern computers and obtain fast data access, locality preserving orderings (LPO) are used to store PMD items. Ordering-based load balancing schemes using locality preserving orderings are fast and appear competitive when the domain is non-convex and highly irregular. Our dynamic data management and load balancing schemes are integrated in AFEAPI (Adaptive Finite Element Application Programmers Interface) and tested on model problems. Numerical results show that our dynamic data management and load balancing schemes are very efficient.