## Details

Original language | English |
---|---|

Article number | 109022 |

Number of pages | 28 |

Journal | Computer physics communications |

Volume | 296 |

Early online date | 23 Nov 2023 |

Publication status | Published - Mar 2024 |

## Abstract

The article presents a strategy and its algorithm to compile a simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The framework addresses state-of-the-art PDE solvers for computational science and engineering applications. An important characteristic of such applications is that the spatial size of the data is often time-invariant and significantly exceeds the temporal size due to the large computational grid in 3D applications. Typical examples, which are also considered in this article, relate to results extracted from unsteady flow simulations. Herein, the flow data, which progresses over time, is frequently calculated spatially parallel based on domain decomposition strategies, which allow to parallelize the simulation on distributed memory machines following a Single Instruction Multiple Data (SIMD) concept. With a view to the memory-efficient reuse of (compressed) simulation results and their CPU time-saving, sufficiently accurate generation, the paper scrutinizes the efficiency of incremental/parallel SVD approaches for such simulation examples. To improve the computational efficiency, the introduction of a bunch matrix is proposed, which enables the aggregation of multiple time steps and SVD updates, and significantly increases the efficiency. The suggested strategy is verified and validated by simple 2D laminar single-phase flows and subsequently applied to more complex 2D and 3D turbulent two-phase flows. Emphasis is given to (a) the accuracy of SVD-based reconstruction, (b) the physical realizability of the reconstructed quantities, (c) the independence of domain partitioning, (d) an efficient snapshot bunching, and (e) related implementation aspects. In addition, the influence of lower and (adaptive) upper rank thresholds on the effort and accuracy is evaluated. A final application renders the practical benefits of the approach and refers to a merchant ship in head waves at Re = 1.4×10^{7} and Fn = 0.26. The simulation involves 2880 processor cores and the related full-rank snapshot matrix has (10^{8}×10^{4}) entries. With a numerical overhead of O(10%), this snapshot matrix can be incrementally generated and compressed by O(95%). The compression is accompanied by only small errors in the integral force and local wave elevation of O(10^{−2}%). This qualifies the method for an efficient subsequent data processing.

## Keywords

- Computational fluid dynamics, Incremental singular value decomposition, Large spatio/temporal data sets, Navier-Stokes flow, Principal component analysis, Reduced order modeling

## ASJC Scopus subject areas

- Computer Science(all)
**Hardware and Architecture****Physics and Astronomy(all)**

## Cite this

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- Apa
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**An incremental singular value decomposition approach for large-scale spatially parallel & distributed but temporally serial data : applied to technical flows.**/ Kühl, Niklas; Fischer, Hendrik; Hinze, Michael et al.

In: Computer physics communications, Vol. 296, 109022, 03.2024.

Research output: Contribution to journal › Article › Research › peer review

*Computer physics communications*, vol. 296, 109022. https://doi.org/10.1016/j.cpc.2023.109022

*Computer physics communications*,

*296*, Article 109022. https://doi.org/10.1016/j.cpc.2023.109022

}

TY - JOUR

T1 - An incremental singular value decomposition approach for large-scale spatially parallel & distributed but temporally serial data

T2 - applied to technical flows

AU - Kühl, Niklas

AU - Fischer, Hendrik

AU - Hinze, Michael

AU - Rung, Thomas

N1 - Funding Information: This paper is a collaborative contribution to the projects M6 and T4 of the Collaborative Research Centre TRR181, “Energy Transfers in Atmosphere and Ocean” funded by German Research Foundation (DFG) under Grant Number 274762653 , which is acknowledged by N.K., M.H. and T.R. The second author (H.F.) acknowledges the funding of the DFG within the framework of the International Research Training Group GRK 2657 “Computational Mechanics Techniques in High Dimensions” under Grant Number 433082294 . The authors gratefully acknowledge the computing time granted by the Resource Allocation Board and provided on the supercomputer Lise and Emmy at NHR@ZIB and NHR@Göttingen as part of the NHR infrastructure. The calculations for this research were conducted with computing resources under the projects hhi00033 (“Hydrodynamic Drag Minimization of Ships”) and hhi00037 (“Energy Fluxes at the Air-Sea Interface”).

PY - 2024/3

Y1 - 2024/3

N2 - The article presents a strategy and its algorithm to compile a simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The framework addresses state-of-the-art PDE solvers for computational science and engineering applications. An important characteristic of such applications is that the spatial size of the data is often time-invariant and significantly exceeds the temporal size due to the large computational grid in 3D applications. Typical examples, which are also considered in this article, relate to results extracted from unsteady flow simulations. Herein, the flow data, which progresses over time, is frequently calculated spatially parallel based on domain decomposition strategies, which allow to parallelize the simulation on distributed memory machines following a Single Instruction Multiple Data (SIMD) concept. With a view to the memory-efficient reuse of (compressed) simulation results and their CPU time-saving, sufficiently accurate generation, the paper scrutinizes the efficiency of incremental/parallel SVD approaches for such simulation examples. To improve the computational efficiency, the introduction of a bunch matrix is proposed, which enables the aggregation of multiple time steps and SVD updates, and significantly increases the efficiency. The suggested strategy is verified and validated by simple 2D laminar single-phase flows and subsequently applied to more complex 2D and 3D turbulent two-phase flows. Emphasis is given to (a) the accuracy of SVD-based reconstruction, (b) the physical realizability of the reconstructed quantities, (c) the independence of domain partitioning, (d) an efficient snapshot bunching, and (e) related implementation aspects. In addition, the influence of lower and (adaptive) upper rank thresholds on the effort and accuracy is evaluated. A final application renders the practical benefits of the approach and refers to a merchant ship in head waves at Re = 1.4×107 and Fn = 0.26. The simulation involves 2880 processor cores and the related full-rank snapshot matrix has (108×104) entries. With a numerical overhead of O(10%), this snapshot matrix can be incrementally generated and compressed by O(95%). The compression is accompanied by only small errors in the integral force and local wave elevation of O(10−2%). This qualifies the method for an efficient subsequent data processing.

AB - The article presents a strategy and its algorithm to compile a simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The framework addresses state-of-the-art PDE solvers for computational science and engineering applications. An important characteristic of such applications is that the spatial size of the data is often time-invariant and significantly exceeds the temporal size due to the large computational grid in 3D applications. Typical examples, which are also considered in this article, relate to results extracted from unsteady flow simulations. Herein, the flow data, which progresses over time, is frequently calculated spatially parallel based on domain decomposition strategies, which allow to parallelize the simulation on distributed memory machines following a Single Instruction Multiple Data (SIMD) concept. With a view to the memory-efficient reuse of (compressed) simulation results and their CPU time-saving, sufficiently accurate generation, the paper scrutinizes the efficiency of incremental/parallel SVD approaches for such simulation examples. To improve the computational efficiency, the introduction of a bunch matrix is proposed, which enables the aggregation of multiple time steps and SVD updates, and significantly increases the efficiency. The suggested strategy is verified and validated by simple 2D laminar single-phase flows and subsequently applied to more complex 2D and 3D turbulent two-phase flows. Emphasis is given to (a) the accuracy of SVD-based reconstruction, (b) the physical realizability of the reconstructed quantities, (c) the independence of domain partitioning, (d) an efficient snapshot bunching, and (e) related implementation aspects. In addition, the influence of lower and (adaptive) upper rank thresholds on the effort and accuracy is evaluated. A final application renders the practical benefits of the approach and refers to a merchant ship in head waves at Re = 1.4×107 and Fn = 0.26. The simulation involves 2880 processor cores and the related full-rank snapshot matrix has (108×104) entries. With a numerical overhead of O(10%), this snapshot matrix can be incrementally generated and compressed by O(95%). The compression is accompanied by only small errors in the integral force and local wave elevation of O(10−2%). This qualifies the method for an efficient subsequent data processing.

KW - Computational fluid dynamics

KW - Incremental singular value decomposition

KW - Large spatio/temporal data sets

KW - Navier-Stokes flow

KW - Principal component analysis

KW - Reduced order modeling

UR - http://www.scopus.com/inward/record.url?scp=85178039733&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2023.109022

DO - 10.1016/j.cpc.2023.109022

M3 - Article

AN - SCOPUS:85178039733

VL - 296

JO - Computer physics communications

JF - Computer physics communications

SN - 0010-4655

M1 - 109022

ER -