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

arXiv: https://arxiv.org/abs/1810.11883 · HTML: https://mlsanity.com/paper/1810.11883/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2603.24196/) (2026)

## Abstract (arXiv)

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.