R-Adaptivity to Enable Compression of Elementary Computations in Extreme-Scale Finite Element Simulators

Technical Report · Sun Sep 01 04:00:00 EDT 2024

DOI:https://doi.org/10.2172/2480161· OSTI ID:2480161

Harper, Graham Bennett ^[1]; Ridzal, Denis ^[1]; Tuminaro, Raymond Stephen ^[1]; Wildey, Timothy Michael ^[1]

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1. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in processing power, the available system memory has not increased commensurately, and electrical power consumption continues to grow. A predominant approach to limit the memory usage in large-scale applications is to exploit the abundant processing power and continually recompute many low-level simulation quantities, rather than storing them. However, this approach can adversely impact the throughput of the simulation and diminish the benefits of modern computing architectures. We present three novel contributions to reduce the memory burden while maintaining, and sometimes improving, performance in simulations based on finite element discretizations. The first contribution develops dictionary-based data compression schemes that detect and exploit the structure of the discretization, due to redundancies across the finite element mesh. While these schemes are shown to reduce memory requirements by more than 99% on meshes with large numbers of identical mesh cells, there are applications where this structure does not exist. The second contribution leverages a recently developed augmented Lagrangian optimization algorithm to enable r-adaptivity for meshes with the goal of enhancing the redundancies in the mesh. The third contribution extends these methods to patch-based linear solvers and preconditioners by compressing local matrices. Numerical results demonstrate the effectiveness of the proposed methods to detect, enhance and exploit mesh structure on a suite of examples inspired by large-scale applications.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
• DOE Contract Number: NA0003525
• OSTI ID: 2480161
• Report Number(s): SAND--2024-13251R
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING