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Topology optimization (TO) can be viewed as seeking an optimal solution in the design space of a given TO problem. For weakly non-linear TO problems, e.g., compliance minimization, sensitivity-based methods typically converge well, whereas…

Optimization and Control · Mathematics 2026-03-25 Ziliang Wang , Jiahua Wu , Jun Yang , Shintaro Yamasaki

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…

Numerical Analysis · Computer Science 2015-02-04 Benjamin Marussig , Jürgen Zechner , Gernot Beer , Thomas-Peter Fries

An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…

Numerical Analysis · Mathematics 2018-06-27 Jorgen S. Dokken , Simon W. Funke , August Johansson , Stephan Schmidt

A multiobjective optimization method is proposed for obtaining the optimal plane trusses simultaneously for various aspect ratios of the initial ground structure as a set of Pareto optimal solutions generated through a single optimization…

Optimization and Control · Mathematics 2023-08-01 Makoto Ohsaki , Saku Aoyagi , Kazuki Hayashi

We investigate a fixed domain approach in shape optimization, using a regularization of the Heaviside function both in the cost functional and in the state system. We consider the compliance minimization problem in linear elasticity, a well…

Optimization and Control · Mathematics 2020-04-07 Cornel Marius Murea , Dan Tiba

With the emergence of new photonic and plasmonic materials with optimized properties as well as advanced nanofabrication techniques, nanophotonic devices are now capable of providing solutions to global challenges in energy conversion,…

We introduce a new "subpixel-smoothed projection" (SSP) formulation for differentiable binarization in topology optimization (TopOpt) as a drop-in replacement for previous projection schemes, which suffer from near-non-differentiability and…

This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…

Optimization and Control · Mathematics 2025-07-23 Huangxin Chen , Piaopiao Dong , Dong Wang , Xiao-Ping Wang

In this paper, a topology optimization framework utilizing automatic differentiation is presented as an efficient way for solving 2D density-based topology optimization problem by calculating gradients through the fully differentiable…

Computational Engineering, Finance, and Science · Computer Science 2020-09-23 Liang Chen , Herman M. H. Shen

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

This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…

Numerical Analysis · Mathematics 2025-07-11 Anna Yesypenko , Chao Chen , Per-Gunnar Martinsson

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Dynamical Systems · Mathematics 2020-02-04 Andreas Bittracher , Stefan Klus , Boumediene Hamzi , Péter Koltai , Christof Schütte

In this work we consider topology optimization of systems, which are governed by the external Bernoulli free boundary problem. We utilize the so-called pseudo-solid approach to solve the governing free boundary problems during the…

Numerical Analysis · Mathematics 2015-03-17 J. I. Toivanen , R. A. E. Makinen , J. Haslinger

It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…

Numerical Analysis · Mathematics 2016-12-28 Paola F. Antonietti , Matteo Bruggi , Simone Scacchi , Marco Verani

Topology optimization using gradient search with negative and positive elliptical masks and honeycomb tessellation is presented. Through a novel skeletonization algorithm for topologies defined using filled and void hexagonal…

Computational Engineering, Finance, and Science · Computer Science 2020-10-13 Nikhil Singh , Prabhat Kumar , Anupam Saxena

We develop and apply a novel shape optimization exemplified for a two-blade rotor with respect to the figure of merit ($FM$). This topologically assisted optimization (TAO) contains two steps. First a global evolutionary optimization is…

The field of optimal design of linear elastic structures has seen many exciting successes that resulted in new architected materials and structural designs. With the availability of cloud computing, including high-performance computing,…

Computational Engineering, Finance, and Science · Computer Science 2021-02-09 Diab W. Abueidda , Seid Koric , Nahil A. Sobh

Multiply connected freeform surface features are widely encountered in industrial components, where toolpath generation often suffers from discontinuities, sharp turns, non-uniform scallop heights, and incomplete boundary coverage. This…

Robotics · Computer Science 2026-04-27 Shen Changqing , Xu Bingzhou , Qi Bosong , Zhang Xiaojian , Yan Sijie , Ding Han

Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…

Optimization and Control · Mathematics 2022-07-26 Volker Schulz , Matthias Schuster , Christian Vollmann

We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…

Numerical Analysis · Mathematics 2026-05-15 Peter Gangl , Brendan Keith , Dohyun Kim , Boyan S. Lazarov , Thomas M. Surowiec