Optimal Polynomial Smoothers for Parallel AMG
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916786181505024 |
|---|---|
| author | D'Ambra, Pasqua Durastante, Fabio Filippone, Salvatore Massei, Stefano Thomas, Stephen |
| author_facet | D'Ambra, Pasqua Durastante, Fabio Filippone, Salvatore Massei, Stefano Thomas, Stephen |
| contents | In this paper, we explore polynomial accelerators that are well-suited for parallel computations, specifically as smoothers in Algebraic MultiGrid (AMG) preconditioners. These accelerators address a minimax problem, initially formulated in [Lottes, Numer. Lin. Alg. with Appl. 30(6), 2518 (2023)], aiming to achieve an optimal (or near-optimal) bound for a polynomial-dependent constant involved in the AMG V-cycle error bound, without requiring information about the matrices' spectra. Lottes focuses on Chebyshev polynomials of the 4th-kind and defines the relevant recurrence formulas applicable to a general convergent basic smoother. In this paper, we demonstrate the efficacy of these accelerations for large-scale applications on modern GPU-accelerated supercomputers. Furthermore, we formulate a variant of the aforementioned minimax problem, which naturally leads to solutions relying on Chebyshev polynomials of the 1st-kind as accelerators for a basic smoother. For all the polynomial accelerations, we describe efficient GPU kernels for their application and demonstrate their comparable effectiveness on standard benchmarks at very large scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Polynomial Smoothers for Parallel AMG D'Ambra, Pasqua Durastante, Fabio Filippone, Salvatore Massei, Stefano Thomas, Stephen Numerical Analysis 65F10, 65F08, 65N55, 65Y05 In this paper, we explore polynomial accelerators that are well-suited for parallel computations, specifically as smoothers in Algebraic MultiGrid (AMG) preconditioners. These accelerators address a minimax problem, initially formulated in [Lottes, Numer. Lin. Alg. with Appl. 30(6), 2518 (2023)], aiming to achieve an optimal (or near-optimal) bound for a polynomial-dependent constant involved in the AMG V-cycle error bound, without requiring information about the matrices' spectra. Lottes focuses on Chebyshev polynomials of the 4th-kind and defines the relevant recurrence formulas applicable to a general convergent basic smoother. In this paper, we demonstrate the efficacy of these accelerations for large-scale applications on modern GPU-accelerated supercomputers. Furthermore, we formulate a variant of the aforementioned minimax problem, which naturally leads to solutions relying on Chebyshev polynomials of the 1st-kind as accelerators for a basic smoother. For all the polynomial accelerations, we describe efficient GPU kernels for their application and demonstrate their comparable effectiveness on standard benchmarks at very large scales. |
| title | Optimal Polynomial Smoothers for Parallel AMG |
| topic | Numerical Analysis 65F10, 65F08, 65N55, 65Y05 |
| url | https://arxiv.org/abs/2407.09848 |