Two-Level Sketching Alternating Anderson acceleration for Complex Physics Applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909054608080896 |
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| author | Barnafi, Nicolás A. Pasini, Massimiliano Lupo |
| author_facet | Barnafi, Nicolás A. Pasini, Massimiliano Lupo |
| contents | We present a novel two-level sketching extension of the Alternating Anderson-Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multi-physics simulations governed by discretized partial differential equations. Our approach combines a static, physics-based projection that reduces the least-squares problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory-access overhead. The resulting algorithm solves reduced least-squares systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration-without degrading convergence rates-on benchmark problems including Stokes, p-Laplacian, Bidomain, and Navier-Stokes formulations at varying problem sizes. These results demonstrate the method's robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open-source in the AAP.jl library. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-Level Sketching Alternating Anderson acceleration for Complex Physics Applications Barnafi, Nicolás A. Pasini, Massimiliano Lupo Numerical Analysis 65N12, 65N22, 65K10, 65F10, 65F99, 65B99 We present a novel two-level sketching extension of the Alternating Anderson-Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multi-physics simulations governed by discretized partial differential equations. Our approach combines a static, physics-based projection that reduces the least-squares problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory-access overhead. The resulting algorithm solves reduced least-squares systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration-without degrading convergence rates-on benchmark problems including Stokes, p-Laplacian, Bidomain, and Navier-Stokes formulations at varying problem sizes. These results demonstrate the method's robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open-source in the AAP.jl library. |
| title | Two-Level Sketching Alternating Anderson acceleration for Complex Physics Applications |
| topic | Numerical Analysis 65N12, 65N22, 65K10, 65F10, 65F99, 65B99 |
| url | https://arxiv.org/abs/2505.08587 |