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This paper presents a highly efficient method to obtain high-resolution, near-optimal 3D topologies optimized for minimum compliance on a standard PC. Using an implicit geometry description we derive a single-scale interpretation of optimal…

Computational Engineering, Finance, and Science · Computer Science 2020-04-22 Jeroen Groen , Florian Stutz , Niels Aage , J. Andreas Bærentzen , Ole Sigmund

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

Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…

Analysis of PDEs · Mathematics 2023-07-10 Stefano Almi , Ulisse Stefanelli

We exploit level set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level set function, geometry, and solution field are parameterized using the non-uniform rational B-spline…

Computational Engineering, Finance, and Science · Computer Science 2023-03-08 Chintan Jansari , Stéphane P. A. Bordas , Elena Atroshchenko

We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…

Optimization and Control · Mathematics 2020-06-24 Peter Gangl

This paper presents a homogenized topology optimization (TO) method for spatially optimizing cell-size distribution of triply-periodic minimal surface (TPMS) structures, with high accuracy in the optimized structural response after…

Optimization and Control · Mathematics 2026-05-08 Hiroki Kawabe , Kaito Ohtani , Yusibo Yang , Musaddiq Al Ali , Kentaro Yaji

This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function {\phi}ij represents the boundary between materials i and j.…

Computational Engineering, Finance, and Science · Computer Science 2022-03-10 Masaki Noda , Yuki Noguchi , Takayuki Yamada

Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures, a novel asymptotic homogenisation topology optimisation…

Computational Engineering, Finance, and Science · Computer Science 2019-12-18 Dingchuan Xue , Yichao Zhu , Shaoshuai Li , Chang Liu , Weisheng Zhang , Xu Guo

We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid…

Computational Engineering, Finance, and Science · Computer Science 2021-05-21 Li Zheng , Siddhant Kumar , Dennis M. Kochmann

A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…

Numerical Analysis · Mathematics 2025-12-24 Wei Xie , Viet Ha Hoang , Yin Yang , Yunqing Huang

We propose a novel level set-based topology optimization for micropolar solids subjected to thermo-mechanical loading. To capture the size effects, we have incorporated the microstructural length-scale information into the level set-based…

Computational Physics · Physics 2026-01-21 Mayank Shekhar , Ayyappan Unnikrishna Pillai , Subhayan De , Mohammad Masiur Rahaman

This paper focuses on the topology optimization of a broadband acoustic transition section that connects two cylindrical waveguides with different radii. The primary objective is to design a transition section such that it maximizes the…

Optimization and Control · Mathematics 2023-10-10 Abbas Mousavi , Andrian Uihlein , Lukas Pflug , Eddie Wadbro

Topological photonics and acoustics have recently garnered wide research interests for their topological ability to manipulate the light and sound at surfaces. Conventionally, the supercell technique is the standard approach to calculating…

Optics · Physics 2025-12-24 Yi-Xin Sha , Ming-Yao Xia , Ling Lu , Yi Yang

In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…

Computational Engineering, Finance, and Science · Computer Science 2019-10-09 Nicolò Pollini , Oded Amir

Topology optimization problems usually feature multiple local minimizers. To guarantee convergence to local minimizers that perform best globally or to find local solutions that are desirable for practical applications due to easy…

Optimization and Control · Mathematics 2025-11-06 Leon Baeck , Sebastian Blauth , Christian Leithäuser , René Pinnau , Kevin Sturm

In the present paper, a new three-scale asymptotic homogenization method is proposed to study the electrical behavior of the cardiac tissue structure with multiple heterogeneities at two different levels. The first level is associated with…

Analysis of PDEs · Mathematics 2022-01-11 Fakhrielddine Bader , Mostafa Bendahmane , Mazen Saad , Raafat Talhouk

We propose a method to modify a polygonal mesh in order to fit the zero-isoline of a level set function by extending a standard body-fitted strategy to a tessellation with arbitrarily-shaped elements. The novel level set-fitted approach, in…

Computational Engineering, Finance, and Science · Computer Science 2023-11-03 Nicola Ferro , Stefano Micheletti , Nicola Parolini , Simona Perotto , Marco Verani , Paola Francesca Antonietti

At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of…

Computational Engineering, Finance, and Science · Computer Science 2020-02-19 Hayoung Chung , Oded Amir , H. Alicia Kim

The level-set method of topology optimization is used to design isotropic two-phase periodic multifunctional composites in three dimensions. One phase is stiff and insulating whereas the other is conductive and mechanically compliant. The…

Materials Science · Physics 2007-12-20 V. J. Challis , A. P. Roberts , A. H. Wilkins

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…

Materials Science · Physics 2024-08-28 Harikrishnan Vijayakumaran , Jonathan B. Russ , Glaucio H. Paulino , Miguel A. Bessa