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We review some recent advances in the field of element-based algebraic stabilization for continuous finite element discretizations of nonlinear hyperbolic problems. The main focus is on multidimensional convex limiting techniques designed…

Numerical Analysis · Mathematics 2026-02-17 Dmitri Kuzmin

Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…

Computational Engineering, Finance, and Science · Computer Science 2024-10-29 Anna Dalklint , Rasmus E. Christiansen , Ole Sigmund

Solving dynamic topology optimization problems often yields low-performing local optima. Instead of converging towards a design that exploits dynamic mechanisms, a less interesting, mass-driven solution is often generated. This necessitates…

Optimization and Control · Mathematics 2025-09-30 Tom De Weer , Vanessa Cool , Elke Deckers

A persistent challenge with the development of electric vertical take-off and landing vehicles (eVTOL) to meet flight power and energy demands is the mass of the load and thermal management systems for batteries. One possible strategy to…

Optimization and Control · Mathematics 2023-08-01 Alexandre T. R. Guibert , Murtaza Bookwala , Ashley Cronk , Y. Shirley Meng , H. Alicia Kim

Engineers learn from every design they create, building intuition that helps them quickly identify promising solutions for new problems. Topology optimization (TO) - a well-established computational method for designing structures with…

Computational Engineering, Finance, and Science · Computer Science 2025-02-05 Igor Kuszczak , Gawel Kus , Federico Bosi , Miguel A. Bessa

Topology optimization has emerged as a powerful and increasingly relevant strategy for enhancing the flexibility and efficiency of power system operations. However, solving these problems is computationally demanding due to their…

Optimization and Control · Mathematics 2026-02-11 Salvador Pineda , Juan Miguel Morales

We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how…

Optics · Physics 2019-06-26 Zin Lin , Victor Liu , Raphaël Pestourie , Steven G. Johnson

Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic…

Computational Engineering, Finance, and Science · Computer Science 2021-03-31 Marek Tyburec , Jan Zeman , Martin Doškář , Martin Kružík , Matěj Lepš

In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix topology and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based…

Computational Engineering, Finance, and Science · Computer Science 2022-05-16 Aaditya Chandrasekhar , Amir Mirzendehdel , Morad Behandish , Krishnan Suresh

This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…

Computational Engineering, Finance, and Science · Computer Science 2023-06-07 Guodong Zhang , Kapil Khandelwal , Tong Guo

The continuation method is a popular approach in non-convex optimization and computer vision. The main idea is to start from a simple function that can be minimized efficiently, and gradually transform it to the more complicated original…

Machine Learning · Computer Science 2018-02-13 Ali Shameli , Yasin Abbasi-Yadkori

Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…

Machine Learning · Computer Science 2024-07-26 Leon Herrmann , Ole Sigmund , Viola Muning Li , Christian Vogl , Stefan Kollmannsberger

With the increasing power density of electronics components, the heat dissipation capacity of heat sinks gradually becomes a bottleneck. Many structural optimization methods, including topology optimization, have been widely used for heat…

Fluid Dynamics · Physics 2021-10-07 Tao Zeng , Hu Wang , Mengzhu Yang , Joe Alexandersen

Photonic crystal fibres (PCFs) are optical fibres that guide light using a modulated dielectric medium. They provide an exceptionally versatile platform for various applications, thanks to the flexibility with which light-guiding can be…

Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior…

Graphics · Computer Science 2024-07-25 Davi Colli Tozoni , Zizhou Huang , Daniele Panozzo , Denis Zorin

We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…

Optimization and Control · Mathematics 2017-10-11 Xiaojia Zhang , Eric de Sturler , Glaucio H. Paulino

Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…

Numerical Analysis · Mathematics 2022-03-17 Vidhi Zala , Robert M. Kirby , Akil Narayan

Topology optimization facilitates the automated design of high-performance structures across various engineering fields but, if unconstrained, often produces designs that are complex and difficult to manufacture. A key attribute of the…

Applied Physics · Physics 2025-04-25 Vanessa Cool , Niels Aage , Ole Sigmund

Transmission topology control is a tool used by system operators in the role of a control action taken into account as a preventive or corrective action relative to a specific outage or set of outages. However, their inclusion in most…

Systems and Control · Electrical Eng. & Systems 2021-03-30 Emily Little , Sandrine Bortolotti , Jean-Yves Bourmaud , Efthymios Karangelos , Yannick Perez

Topology Optimization (TO), which maximizes structural robustness under material weight constraints, is becoming an essential step for the automatic design of mechanical parts. However, existing TO algorithms use the Finite Element Analysis…

Robotics · Computer Science 2022-04-14 Zherong Pan , Xifeng Gao , Kui Wu