Configurable Open-source Data Structure for Distributed Conforming Unstructured Homogeneous Meshes with GPU Support

Abstract

A general multi-purpose data structure for an efficient representation of conforming unstructured homogeneous meshes for scientific computations on CPU and GPU-based systems is presented. The data structure is provided as open-source software as part of the TNL library (https://tnl-project.org/). The abstract representation supports almost any cell shape and common 2D quadrilateral, 3D hexahedron and arbitrarily dimensional simplex shapes are currently built into the library. The implementation is highly configurable via templates of the C++ language, which allows avoiding the storage of unnecessary dynamic data. The internal memory layout is based on state-of-the-art sparse matrix storage formats, which are optimized for different hardware architectures in order to provide high-performance computations. The proposed data structure is also suitable for meshes decomposed into several subdomains and distributed computing using the Message Passing Interface (MPI). The efficiency of the implemented data structure on CPU and GPU hardware architectures is demonstrated on several benchmark problems and a comparison with another library. Its applicability to advanced numerical methods is demonstrated with an example problem of two-phase flow in porous media using a numerical scheme based on the mixed-hybrid finite element method (MHFEM). We show GPU speed-ups that rise above 20 in 2D and 50 in 3D when compared to sequential CPU computations, and above 2 in 2D and 9 in 3D when compared to 12-threaded CPU computations.

GTMesh: A Highly Efficient C++ Template Library for Numerical Schemes on General Topology Meshes

“…For example, in a 3D mesh, the boundaries of the 3D cells consist of 2D faces, which in turn represent flat surfaces bounded by 1D edges, which in turn span between their two 0D vertices. In order to avoid confusion with the notion of element in FEM, these objects are also called entities [27].…”

“…• MOAB (Mesh-Oriented datABase) [26] is an extensive library that allows general topology meshes and supports mesh refinement, decomposition, parallel I/O and other features. Despite being written in C++, it does not take advantage of templates, and its performance has been shown to be relatively poor when processing polyhedral meshes [27]. MOAB always represents mesh geometry in a 3D coordinate system.…”

“…• TNL (Template Numerical Library) [29] is a dynamically evolving framework for implementing efficient numerical algorithms in C++, taking advantage of State-ofthe-Art C++ programming paradigms and exposing both CPU and GPU programming through a unified interface. Recently, support for general topology polytopal meshes [27] has been added. With all the above in mind, we introduce GTMesh, a library created to facilitate rapid development of numerical schemes and data postprocessing algorithms on general polytopal meshes in an arbitrary dimension.…”