Dynamic Load Balancing Techniques for Nonlinear Structural Dynamics

Abstract

The efficiency of a parallel solution to a numerical problem relies on the distribution of workload among processors. A well-balanced workload yields a more efficient solution than an imbalanced one. Unfortunately, achieving an optimal workload distribution for more than 2 processors is almost intractable because this process requires solving a non-deterministic polynomial (NP) time complete problem. A more amenable approach is to pursue near-optimal distribution using an heuristics-based algorithm. Load balancing algorithms can be classified either as static or dynamic. Static load balancing algorithms distribute tasks among processors during compile time, while dynamic algorithms bind to the processes during run-time. The major advantage of static algorithms is that, unlike dynamic algorithms, they incur no run-time overhead, and are easier to implement. However, they require a priori knowledge about the solution path and the state of the system during processing. This limitation makes dynamic load balancing more favorable for parallel programs which the execution times for processes and their communication requirements cannot be predicted. In Parallel Finite Element Analysis (PFEA), the solution can be parallelized by means of domain partitioning and/or by parallelizing the linear algebra computations. This work focuses on the improvement of domain partitioning-based methods and it takes advantage of parallel linear algebra. In domain partitioning PFEA methods, finite element domain is either partitioned into a number of subdomains equal or larger to the number of processing units. The resulting subsystems are then solved in parallel and their solutions are integrated into the global solution. Manual partitioning of finite element domains is painstaking and seldom produce efficient results, so various automatic partitioning algorithms have been devised to produce near-optimal results by heuristics means. Heuristic domain partitioning algorithms can be classified as topologyor geometrybased, spectral or non-spectral, and recursive or sequential. Topology-based algorithms use topological information of the mesh or its associated graph to partition the domain, while geometry-based algorithms partition domains using the geometrical data of its mesh. Some algorithms use both topological as well as geometrical information to carry out the partitioning. Spectral methods use spectral analysis of the global graph associated with the finite element mesh to locate partition separators, while non-spectral methods 17 ANALYSIS AND COMPUTATION SPECIALTY CONFERENCE th