A Scalable and Modular Software Architecture for Finite Elements on Hierarchical Hybrid Grids

TL;DR

This paper introduces a scalable, modular finite-element software framework optimized for parallel supercomputers, enabling flexible, high-performance simulations of complex PDE systems with adaptable geometries.

Contribution

It presents a novel generic higher-order finite-element framework combining unstructured and structured grids, supporting scalability, flexibility, and efficient multigrid methods for large-scale simulations.

Findings

Achieved high scalability and performance on supercomputers.

Demonstrated flexibility in handling coupled PDE systems.

Showcased applicability to geophysical simulations.

Abstract

In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers. Combining an unstructured topology with structured grid refinement facilitates high geometric adaptability and matrix-free multigrid implementations with excellent performance. Different abstraction levels and fully distributed data structures additionally ensure high flexibility, extensibility, and scalability. The software concepts support sophisticated load balancing and flexibly combining finite element spaces. Example scenarios with coupled systems of PDEs show the applicability of the concepts to performing geophysical simulations.