Article
Mathematics, Applied
Sebastian Blauth
Summary: The space mapping technique is utilized to solve complex optimization problems efficiently by combining the accuracy of fine model simulations and the speed of coarse model optimizations. This paper proposes novel space mapping methods for shape optimization problems constrained by PDEs, which are presented in a Riemannian setting based on Steklov-Poincare-type metrics. Numerical performance of the methods is investigated on various model problems, demonstrating their great efficiency in solving complex shape optimization problems.
SIAM JOURNAL ON OPTIMIZATION
(2023)
Article
Mathematics, Applied
Davod Khojasteh Salkuyeh, Hamid Mirchi
Summary: We propose a new free-parameter double splitting iteration method for solving linear equations resulting from the finite element discretization of a PDE-constrained optimization problem. We prove that the eigenvalues of the iteration matrix lie in the interval (0, 21], indicating unconditional convergence of the method. Numerical comparison against two existing methods is provided to demonstrate the effectiveness of our approach.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Computer Science, Software Engineering
Deborah B. Gahururu, Michael Hintermueller, Thomas M. Surowiec
Summary: This paper introduces a class of risk-neutral generalized Nash equilibrium problems, in which the feasible strategy set of each player is subject to a common linear elliptic partial differential equation with random inputs. Existence of Nash equilibria and first-order optimality conditions are derived by exploiting higher integrability and regularity of the random field state variables and a specially tailored constraint qualification. A relaxation scheme based on the Moreau-Yosida approximation is proposed, and the numerical algorithms for both individual player problems and the GNEP as a whole are demonstrated to be viable through several examples.
MATHEMATICAL PROGRAMMING
(2023)
Article
Mathematics, Applied
Ryan H. Vogt, Sven Leyffer, Todd S. Munson
Summary: In this paper, a mixed-integer partial differential equation constrained optimization problem is formulated for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. The formulation is extended to include uncertainty with respect to the angle of the incidence wave, and a mixed-integer trust-region approach is developed for solving both the deterministic and uncertain formulation. Detailed numerical results demonstrate the effectiveness of the trust-region approach in obtaining effective cloaks.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Liang Fang, Stefan Vandewalle, Johan Meyers
Summary: Multiple shooting methods have been rapidly developed as a promising approach to optimize the solution to optimal control problems. In this study, we propose a new multiple shooting algorithm based on a sequential quadratic programming method, which is suitable for large-scale time-dependent PDEs. We analyze the KKT matrix structure and solve the large-scale KKT system using a preconditioned conjugate gradient algorithm. The algorithm is validated on two control problems and achieves considerable accelerations compared to single shooting approaches.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Liang Fang, Stefan Vandewalle, Johan Meyers
Summary: This study proposes a new parallel-in-time multiple shooting algorithm for solving large scale optimal control problems governed by parabolic PDEs. The algorithm is validated and analyzed using different test cases, showing significant speed-ups and better performance for complex flow fields.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Software Engineering
Sebastian Blauth
Summary: This paper introduces version 2.0 of cashocs, a software for solving PDE constrained optimization problems in shape optimization and optimal control. The software has added many new features and tools, including a framework for space mapping, solving topology optimization problems with a level-set approach, parallel support via MPI, and the ability to handle additional constraints.
Article
Mathematics, Applied
Alexandra Buenger, Valeria Simoncini, Martin Stoll
Summary: The study proposes a new framework for efficiently computing a low-rank approximation to the solution by reformulating the KKT system into a Sylvester-like matrix equation, providing a solution to the challenges of PDE-constrained optimization problems. By implementing a Galerkin condition and an iterative rational Krylov method, a reduced problem is obtained, improving computational efficiency.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Artificial Intelligence
Cong Wang, Shengyuan Xu
Summary: This study investigates multiagent distributed online constrained convex optimization problems with feedback delays and communication topologies between nodes. By using the distributed online primal-dual bandit push-sum algorithm with delayed feedback, metrics for measuring algorithm performance are proposed and the theoretical results are validated through simulations.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Mathematics, Applied
Dominik Garmatter, Margherita Porcelli, Francesco Rinaldi, Martin Stoll
Summary: This article investigates penalization techniques as an alternative solution approach for optimal control problems with PDE and integer constraints. A novel improved penalty algorithm is proposed, incorporating a basin hopping strategy and an interior point method specialized for the problem class. Thorough numerical investigations demonstrate the versatility of the approach.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Physics, Applied
Blake A. Wilson, Zhaxylyk A. Kudyshev, Alexander V. Kildishev, Sabre Kais, Vladimir M. Shalaev, Alexandra Boltasseva
Summary: In this work, a machine learning-based framework was developed to map continuous-space inverse design problems into binary optimization problems. By repeatedly resampling and retraining the factorization machine, designs with superior figures of merit were achieved.
APPLIED PHYSICS REVIEWS
(2021)
Article
Engineering, Multidisciplinary
Sun-Yong Kim
Summary: CSFM method is proposed to save computational expenses in topology optimization. It controls the change of filtered sensitivity values based on previous iterations, resulting in lower compliance and reduced computational expenses.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Sebastian Blauth
Summary: In this paper, nonlinear conjugate gradient methods based on Steklov-Poincare-type metrics are proposed for solving shape optimization problems constrained by partial differential equations. The numerical comparison shows that these methods perform well in practice, making them an efficient and attractive addition to gradient-based shape optimization algorithms.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Multidisciplinary Sciences
Carlo Sinigaglia, Davide E. Quadrelli, Andrea Manzoni, Francesco Braghin
Summary: This paper demonstrates an efficient approach to achieve thermal cloaking by controlling the distribution of active heat sources. By formulating the problem as a PDE-constrained optimization, the goal is to actuate the space-time control field so that the thermal field outside the obstacle is indistinguishable from the reference field. To tackle this problem rapidly and reliably, a parametrized reduced order model is utilized, providing significant computational speedups compared to a high-fidelity, full-order model.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Nirmal Kumar, Sanat Kumar Mahato, Asoke Kumar Bhunia
Summary: This article aims to design an algorithm based on binary tournament process using two different types of metaheuristic algorithms. The proposed algorithm is applied on partial differential equation constrained optimization problems and compared with existing algorithms. Nonparametric statistical tests are performed to check the significance of the results.
APPLIED SOFT COMPUTING
(2022)
Article
Chemistry, Multidisciplinary
Fengwen Wang, Marie Brons, Ole Sigmund
Summary: Stretch-dominated truss and plate microstructures are competing in the development of highly rigid and strong architected materials. Although closed-cell isotropic plate microstructures meet theoretical upper bounds on stiffness, they have low buckling strength, whereas open-cell truss microstructures have high buckling strength but reduced stiffness. Hollow truss lattice and hierarchical microstructures outperform both in terms of buckling strength, but are challenging to build. In this study, single-scale non-hierarchical microstructures are designed, built, and tested, surpassing the buckling strength of hollow truss lattice and plate microstructures. The microstructures are realized with 3D printing and both experiments and numerical modeling validate the theoretical predictions.
ADVANCED FUNCTIONAL MATERIALS
(2023)
Article
Optics
Rasmus E. Christiansen, Philip Trost Kristensen, Jesper Mork, Ole Sigmund
Summary: Using topology optimization, compact wavelength-sized devices are designed to study the effect of optimizing geometries for enhancing different optical processes. The findings show that different field distributions lead to maximization of different processes, emphasizing the importance of targeting the appropriate metric when designing photonic components for optimal performance.
Article
Computer Science, Interdisciplinary Applications
Brice Rogie, Casper Schousboe Andreasen
Summary: This paper demonstrates the advantages of topology optimization of heat sinks, beyond the capabilities of pseudo 3D models. It investigates the use of 3D effects for microchannel heat sinks and compares them to state-of-the-art industrial designs for microelectronic applications. The study shows that the performance of microchannel heat sinks highly depends on complex refrigerant distribution and intricate flow paths, and a 3D topology optimized microchannel heat sink can significantly reduce the temperature elevation of a microelectronic chip.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Engineering, Multidisciplinary
Yafeng Wang, Ole Sigmund
Summary: This study aims to optimize the buckling capacity of mechanical structures subjected to thermal and mechanical loading through a density-based topology optimization scheme. By decoupling the effects of mechanical and thermal loadings, the buckling aspects induced by each loading can be separately analyzed and optimized. The study also employs a multi-material topology optimization scheme to optimize the buckling capacity of active structures and prestressed structures.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Erik A. Traff, Anton Rydahl, Sven Karlsson, Ole Sigmund, Niels Aage
Summary: This work presents three-dimensional linear elastic compliance minimisation using topology optimisation implementations accelerated by Graphics Processing Units (GPUs). Two GPU-accelerated implementations, based on OpenMP 4.5 and the Futhark language, are presented. Both implementations utilize high level GPU frameworks, avoiding the need for expertise knowledge of CUDA or OpenCL. Additionally, a vectorised and multi-threaded CPU code is included for reference. The results show that the GPU accelerated codes are able to solve large-scale topology optimisation problems faster than the reference CPU code, and they can also handle nonlinear problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Christoffer Fyllgraf Christensen, Fengwen Wang, Ole Sigmund
Summary: Topology optimization has been used for maximizing stiffness or minimizing compliance in multiscale structures. This study focuses on optimizing buckling stability of multiscale structures with isotropic porous infill, by considering both local and global instability.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Federico Ferrari, Ole Sigmund
Summary: In this study, a strategy is introduced to prevent the occurrence of spurious modes in the spectrum computed by linearized buckling analysis in the context of topology optimization. Spurious buckling modes commonly appear in low density regions, but this study also highlights the occurrence of localized modes in solid areas due to the limitations of linearized buckling analysis. The proposed remedy involves using filtering and erosion operations on the stress field, helping to mitigate the occurrence of spurious modes and improve the optimization process towards high performance designs.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Acoustics
Peter Risby Andersen, Vicente Cutanda Henriquez, Niels Aage
Summary: The increasing interest in miniaturizing acoustic devices has highlighted the importance of accurate and efficient models of acoustic viscous and thermal losses, especially in micro-acoustic devices. While using the full linearized Navier Stokes equations for modeling losses is computationally expensive, the use of an approximate boundary layer impedance boundary condition has become popular due to its high efficiency. However, applying the boundary layer impedance can be problematic when boundary layers overlap, impacting optimization results and design possibilities.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Lukas C. Hoghoj, Cian Conlan-Smith, Ole Sigmund, Casper Schousboe Andreasen
Summary: This paper presents a method for simultaneous optimization of the outer shape and internal topology of aircraft wings, with the objective of minimizing drag subject to lift and compliance constraints for multiple load cases. The physics are evaluated by the means of a source-doublet panel method for the aerodynamic response and linear elastic finite elements for the structural response, which are one-way coupled. Wings of small fixed-wing airplanes both with and without a stiffening strut are optimized. The resulting wings show internal topologies with struts and wall-truss combinations, depending on the design freedom of the shape optimization. The lift distributions of the optimized wings show patterns like the ones obtained when performing optimization of wing shapes with constraints on the bending moment at the root.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Energy & Fuels
Vaishnavi Kale, Niels Aage, Marc Secanell
Summary: A variable density, stress-constrained topology optimization approach is used to optimize the rotor of a flywheel energy storage system (FESS). A new specific energy maximization optimization formulation is proposed to eliminate the need for an arbitrary volume fraction constraint. Factors such as operating speed, maximum stress, rotational symmetry, and rotor material are investigated to understand their effects on optimal topology and energy capacity.
JOURNAL OF ENERGY STORAGE
(2023)
Article
Engineering, Multidisciplinary
Weichen Li, Yingqi Jia, Fengwen Wang, Ole Sigmund, Xiaojia Shelly Zhang
Summary: This study systematically investigates several precisely programmed nonlinear extreme responses in 3D structures under finite deformations through multimaterial inverse design by topology optimization. Unique complex 3D geometries with deformation capabilities are discovered and utilized to deliver the target responses. The optimized structure is accurately fabricated through a proposed hybrid fabrication method and the design's programmed behavior is validated.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Acoustics
Peter Risby Andersen, Gyeong-Tae Lee, Daniel Gert Nielsen, Junghwan Kook, Vicente Cutanda Henriquez, Niels Aage, Yong-Hwa Park
Summary: This work focuses on the shape optimization and experimental validation of an acoustic lens for compact loudspeakers, such as those used in speakerphones. The optimization uses a combined lumped parameter and boundary element method model with a free form deformation geometry parameterization. The optimized design is 3D printed and characterized experimentally to verify its frequency response. The results show good agreement between measurements and simulations, although some shortcomings of the model assumptions are revealed.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2023)
Article
Engineering, Multidisciplinary
Rebekka Woldseth, J. Andreas Baerentzen, Ole Sigmund
Summary: This paper presents an alternative approach to dehomogenisation of elastic Rank-N laminate structures based on the computer graphics discipline of phasor noise. The proposed methodology offers an improvement of existing methods, where high-quality single-scale designs can be obtained efficiently without the utilisation of any least-squares problem or pre-trained models. Numerical tests verifies the performance of the proposed methodology compared to state-of-the-art alternatives, and the dehomogenised designs achieve structural performance within a few percentages of the optimised homogenised solution.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
