Monolithic Library Based on Graph Structure for Parallel Simulation with Domain Decomposition Method and its Application to Various Numerical Methods

Abstract

This paper provides a survey on prominent libraries that enable parallel simulations, with a focus on their applicability for research and development purposes. It discusses the functionalities and scope of these libraries with respect to range of numerical methods to which they can be applied. Following an overview and discussion of libraries, this paper introduces a unified library designed for domain-decomposition based parallel simulations. The unified library is based on graph structures representing the interactions between computational points in numerical simulations, aiming to be applicable to a wide variety of numerical methods. As applications of the graph-based unified library, the paper presents standard finite element method (mesh-based method), particle method (mesh-free method), and s-version finite element method that allows for the overlay of multiple meshes within the finite element framework. The parallel computing performance of these methods is also discussed.