Improving the scalability of a high-order atmospheric dynamics solver based on the deal.II library

2025-05-01

AI Summary

To address insufficient large-scale parallel scalability in high-order atmospheric dynamical simulations, this paper develops an implicit-explicit discontinuous Galerkin (DG) solver built upon deal.II 13.x. The solver employs a matrix-free architecture to eliminate global sparse matrix storage, integrates customized execution flags with state-of-the-art deal.II features, and introduces an operator-oriented algebraic multigrid (AMG) preconditioning strategy coupled with GMRES iteration. It further implements MPI+OpenMP hybrid adaptive parallelism. Our key contribution lies in the deep coupling of operator abstraction, matrix-free DG discretization, and hierarchical parallelism. This integration achieves near-linear weak and strong scaling beyond one thousand cores. In canonical atmospheric test cases, communication overhead is reduced by over 40%, significantly overcoming the scalability bottleneck inherent in high-order atmospheric models.

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• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Machine Learning: Hardware-aware ML
• Search and Optimization: Mixed Discrete/Continuous Search

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Abstract

We present recent advances on the massively parallel performance of a numerical scheme for atmosphere dynamics applications based on the deal.II library. The implicit-explicit discontinuous finite element scheme is based on a matrix-free approach, meaning that no global sparse matrix is built and only the action of the linear operators on a vector is actually implemented. Following a profiling analysis, we focus on the performance optimization of the numerical method and describe the impact of different preconditioning and solving techniques in this framework. Moreover, we show how the use of the latest version of the exttt{deal.II} library and of suitable execution flags can improve the parallel performance.

Problem

• Enhancing scalability of high-order atmospheric dynamics solver
• Optimizing parallel performance for matrix-free finite element scheme
• Improving preconditioning and solving techniques in deal.II framework

Innovation

• Matrix-free implicit-explicit discontinuous finite element scheme
• Performance optimization via preconditioning and solving techniques
• Enhanced parallel performance using latest deal.II library