FFT, FMM, and Multigrid on the Road to Exascale: performance challenges and opportunities

TL;DR

This paper compares FFT, FMM, and multigrid methods for elliptic PDEs, analyzing their scalability and performance challenges on future exascale systems with complex architectures.

Contribution

It provides a model-based comparison and performance predictions for these methods in the context of exascale computing constraints.

Findings

Identifies key challenges for FFT, FMM, and multigrid on exascale systems.

Uses performance models to predict scalability and efficiency.

Highlights the importance of addressing concurrency, resilience, and energy efficiency.

Abstract

FFT, FMM, and multigrid methods are widely used fast and highly scalable solvers for elliptic PDEs. However, emerging large-scale computing systems are introducing challenges in comparison to current petascale computers. Recent efforts (Dongarra et al. 2011) have identified several constraints in the design of exascale software that includes massive concurrency, resilience management, exploiting the high performance of heterogeneous systems, energy efficiency, and utilizing the deeper and more complex memory hierarchy expected at exascale. In this paper, we perform a model-based comparison of the FFT, FMM, and multigrid methods in the context of these projected constraints. In addition, we use performance models to offer predictions about the expected performance on upcoming exascale system configurations based on current technology trends.