On the Implementation of a Scalable Simulator for Multiscale Hybrid-Mixed Methods

TL;DR

This paper develops and compares two scalable simulation prototypes for Multiscale Hybrid-Mixed methods, enabling efficient solutions for heterogeneous problems on coarse meshes in high-performance and cloud computing environments.

Contribution

It introduces two distinct implementation strategies for MHM simulators, integrating C++, Erlang, and MPI to enhance scalability and adaptability across computing platforms.

Findings

Both simulators demonstrate efficient performance in their respective environments.

The multi-language approach enables deployment in cloud and high-performance systems.

The study provides insights into software productivity and fault-tolerance for Exascale computing.

Abstract

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.