Exploiting semantics of temporal multi‐scale methods to optimize multi‐level mesh partitioning

Multi-scale problems are often solved by decomposing the problem domain into multiple subdomains, solving them independently using different levels of spatial and temporal refinement, and coupling the subdomain solutions back to obtain the global solution. Most commonly, finite elements are used for spatial discretization, and finite difference time stepping is used for time integration. Given a finite element mesh for the global problem domain, the number of possible decompositions into subdomains and the possible choices for associated time steps is exponentially large, and the computational costs associated with different decompositions can vary by orders of magnitude. The problem of finding an optimal decomposition and the associated time discretization that minimizes computational costs while maintaining accuracy is nontrivial. Existing mesh partitioning tools, such as METIS, overlook the constraints posed by multi-scale methods and lead to suboptimal partitions with a high performance penalty. We present a multi-level mesh partitioning approach that exploits domain-specific knowledge of multi-scale methods to produce nearly optimal mesh partitions and associated time steps automatically. Results show that for multi-scale problems, our approach produces decompositions that outperform those produced by state-of-the-art partitioners like METIS and even those that are manually constructed by domain experts. Copyright © 2017 John Wiley & Sons, Ltd.