Related papers: Full-Space Approach to Aerodynamic Shape Optimizat…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
Shape optimization has been playing an important role in a large variety of engineering applications. Existing shape optimization methods are generally mesh-dependent and therefore encounter challenges due to mesh deformation. To overcome…
This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation…
The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The extension is based on optimization on Riemannian vector space…
Bayesian optimisation (BO) is a standard approach for sample-efficient global optimisation of expensive black-box functions, yet its scalability to high dimensions remains challenging. Here, we investigate nonlinear dimensionality reduction…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
We compare surface metrics for shape optimization problems with constraints, consisting mainly of partial differential equations (PDE), from a computational point of view. In particular, classical Laplace-Beltrami type based metrics are…
On the one hand, Sobolev gradient smoothing can considerably improve the performance of aerodynamic shape optimization and prevent issues with regularity. On the other hand, Sobolev smoothing can also be interpreted as an approximation for…
This work proposes a windowed least-squares (WLS) approach for model-reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space-time trial…
The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
Bayesian Optimisation (BO) is a state-of-the-art global optimisation technique for black-box problems where derivative information is unavailable, and sample efficiency is crucial. However, improving the general scalability of BO has proved…
Pipe routing is a highly complex, time-consuming, and no-deterministic polynomial-time hard (NP-hard) problem in aeroengine design. Despite extensive research efforts in optimizing constant-curvature pipe routing, the growing demand for…
This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…
Aircraft aerodynamic design optimization must account for the varying operating conditions along the cruise segment as opposed to designing at one fixed operating condition, to arrive at more realistic designs. Conventional approaches…
The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn-Hilliard…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
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…