Balancing Parallel Adaptive FEM Computations by Solving Systems of Linear Equations

• Published in: Euro-Par 2005 Parallel Processing pp. 209 - 219
• Main Authors: Meyerhenke, Henning, Schamberger, Stefan
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Exact sciences and technology; graph partitioning; load balancing; Parallel adaptive FEM computations; Software; Finite element method; High performance; Parallel algorithm; Linear equation; Heuristic method; Parallelism; Parallel computation; Metric; Distributed system; Load balancing; Distributed computing; Adaptive method
• ISBN: 3540287000; 9783540287001
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11549468_26

Load balancing plays an important role in parallel numerical simulations. State-of-the-art libraries addressing this problem base on vertex exchange heuristics that are embedded in a multilevel scheme. However, these are hard to parallelize due to their sequential nature. Furthermore, libraries like Metis and Jostle focus on a small edge-cut and cannot obey constraints like connectivity and straight partition boundaries, which are important for some numerical solvers. In this paper we present an alternative approach to balance the load in parallel adaptive finite element simulations. We compute a distribution that is based on solutions of linear equations. Integrated into a learning framework, we obtain a heuristic that contains a high degree of parallelism and computes well shaped connected partitions. Furthermore, our experiments indicate that we can find solutions that are comparable to those of the two state-of-the-art libraries Metis and Jostle also regarding the classic metrics like edge-cut and boundary length.