On the Implementation of a Scalable Simulator for Multiscale Hybrid-Mixed Methods
This work provides scalable implementations of MHM methods for heterogeneous problems, targeting high-performance and cloud computing environments.
The paper presents two simulator prototypes for Multiscale Hybrid-Mixed (MHM) finite element methods, one using a multi-language approach (C++ and Erlang) and the other a single-language approach (C++ with MPI). Performance evaluation shows both are efficient, with the MPI version achieving up to 90% parallel efficiency on 512 cores.
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on coarse meshes while providing solutions with high-order precision. It embeds independent local problems which are responsible for upscaling unresolved scales into the numerical solution. These local contributions are brought together through a global problem defined on the skeleton of the coarse partition. Since the local problems are completely independent, they can be easily computed in parallel. In this paper, we present two simulator prototypes specifically crafted for the MHM methods, which adopt two different implementation strategies: (i) a multi-programming language approach, each language tackling different simulation issues; and (ii) a classical, single-programming language approach. Specifically, we use C++ for numerical computation of the global and local problems in a modular way; for process distribution in the simulator, we adopt the Erlang concurrent language in the first approach, and the MPI standard in the second approach. The aim of exploring these different approaches is twofold: (i) allow for the deployment of the simulator both in high-performance computing (with MPI) and in cloud computing environments (with Erlang); and (ii) pave the way for further exploration of quality attributes related to software productivity and fault-tolerance, which are key to Exascale systems. We present a performance evaluation of the two simulator prototypes taking into account their efficiency.