Accelerating structural optimization via EIFEM: a ROM-based preconditioner
Abstract
Topology optimization (TopOpt) is a standard tool for structural conceptual design, providing optimal structures with great design freedom. However, it has a high computational costs due to the repeated evaluation of high-fidelity finite element models and frequently produces complex geometries that require extensive interpretation for manufacturability. As an alternative, this work presents a parameterized optimization framework based on Reduced Order Modeling (ROM) and preconditioning techniques. We employ the Empirical Interscale Finite Element Method (EIFEM) coupled with the Discrete Empirical Interpolation Method (DEIM) to construct localized, parameter-dependent reduced operators. From an optimization perspective, this approach can be interpreted as a preconditioning strategy in which inexact gradients are used to accelerate convergence. Furthermore, parameterizing the design space in terms of explicit geometric features, such as inclusion radii or lattice widths, significantly improves the manu facturability of the resulting optimized designs. We assess the performance of the method in terms of computational time, design topology and structural performance with TopOpt as baseline for three differ ent unit cell geometries and three different benchmarks. While the parametric ROM framework requires an initial offline training phase, our comparative analysis demonstrates that it drastically accelerates the online optimization loop and that it can produce even stiffer design in some of our experiments.
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BibTeX
@misc{rubio2026accelerating,
title = {{Accelerating structural optimization via EIFEM: a ROM-based preconditioner}},
author = {Raul Rubio and Alex Ferrer and Joaquin Alberto Hernandez and Pablo Antolin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20053},
eprint = {2609.20053},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20053},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Accelerating structural optimization via EIFEM: a ROM-based preconditioner
AU - Raul Rubio
AU - Alex Ferrer
AU - Joaquin Alberto Hernandez
AU - Pablo Antolin
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20053
UR - https://arxiv.org/abs/2609.20053
AB - Topology optimization (TopOpt) is a standard tool for structural conceptual design, providing optimal structures with great design freedom. However, it has a high computational costs due to the repeated evaluation of high-fidelity finite element models and frequently produces complex geometries that require extensive interpretation for manufacturability. As an alternative, this work presents a parameterized optimization framework based on Reduced Order Modeling (ROM) and preconditioning techniques. We employ the Empirical Interscale Finite Element Method (EIFEM) coupled with the Discrete Empirical Interpolation Method (DEIM) to construct localized, parameter-dependent reduced operators. From an optimization perspective, this approach can be interpreted as a preconditioning strategy in which inexact gradients are used to accelerate convergence. Furthermore, parameterizing the design space in terms of explicit geometric features, such as inclusion radii or lattice widths, significantly improves the manu facturability of the resulting optimized designs. We assess the performance of the method in terms of computational time, design topology and structural performance with TopOpt as baseline for three differ ent unit cell geometries and three different benchmarks. While the parametric ROM framework requires an initial offline training phase, our comparative analysis demonstrates that it drastically accelerates the online optimization loop and that it can produce even stiffer design in some of our experiments.
ER -