Kevin Sturm
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View article: A multimaterial topology optimisation approach to Dirichlet control with piecewise constant functions
A multimaterial topology optimisation approach to Dirichlet control with piecewise constant functions Open
In this paper we study a Dirichlet control problem for the Poisson equation, where the control is assumed to be piecewise constant function which is allowed to take M > 1 different values. The space of admissible Dirichlet controls is non-…
View article: Complete topological asymptotic expansion for L2 and H1 tracking-type cost functionals in dimension two and three
Complete topological asymptotic expansion for L2 and H1 tracking-type cost functionals in dimension two and three Open
In this paper, we study the topological asymptotic expansion of a topology optimisation problem that is constrained by the Poisson equation with the design/shape variable entering through the right hand side. Using an averaged adjoint appr…
View article: A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells
A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells Open
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 manufact…
View article: Minimisation of peak stresses with the shape derivative
Minimisation of peak stresses with the shape derivative Open
This paper is concerned with the minimisation of peak stresses occurring in linear elasticity. We propose to minimise the maximal von Mises stress of the elastic body. This leads to a nonsmooth shape functional. We derive the shape derivat…
View article: Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells
Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells Open
In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We use the Borvall-Petersson model to describe the fluid flow and derive a criterion for a uniform flow distribution in the bipolar pl…
View article: Topology optimization for uniform flow distribution in electrolysis cells
Topology optimization for uniform flow distribution in electrolysis cells Open
In this paper, we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We present a model for the bipolar plate using the Stokes equation with an additional drag term, which models the influence of fluid …
View article: Quasi-Newton methods for topology optimization using a level-set method
Quasi-Newton methods for topology optimization using a level-set method Open
The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for so…
View article: Topology Optimization for Uniform Flow Distribution in Electrolysis Cells
Topology Optimization for Uniform Flow Distribution in Electrolysis Cells Open
In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We present a model for the bipolar plate using the Stokes equation with an additional drag term, which models the influence of fluid a…
View article: The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation
The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation Open
View article: Numerical shape optimization of the Canham-Helfrich-Evans bending energy
Numerical shape optimization of the Canham-Helfrich-Evans bending energy Open
View article: Quasi-Newton Methods for Topology Optimization Using a Level-Set Method
Quasi-Newton Methods for Topology Optimization Using a Level-Set Method Open
The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for so…
View article: Comment on Transverse Charge Density and the Radius of the Proton
Comment on Transverse Charge Density and the Radius of the Proton Open
The charge radius of the proton is typically determined from electron-proton scattering by extracting the proton's electric form factor and then making use of the derivative of that form factor at zero four-momentum transfer. Unfortunately…
View article: The topological state derivative: an optimal control perspective on topology optimisation
The topological state derivative: an optimal control perspective on topology optimisation Open
In this paper we introduce the topological state derivative for general topological dilatations and explore its relation to standard optimal control theory. We show that for a class of partial differential equations, the shape dependent st…
View article: Automated computation of topological derivatives with application to nonlinear elasticity and reaction–diffusion problems
Automated computation of topological derivatives with application to nonlinear elasticity and reaction–diffusion problems Open
While topological derivatives have proven useful in applications of topology\noptimisation and inverse problems, their mathematically rigorous derivation\nremains an ongoing research topic, in particular in the context of nonlinear\npartia…
View article: Topological Derivative for PDEs on Surfaces
Topological Derivative for PDEs on Surfaces Open
In this paper we study the problem of the optimal distribution of two materials on smooth submanifolds $M$ of dimension $d-1$ in $\mathbf R^d$ without boundary by means of the topological derivative. We consider a class of shape optimisati…
View article: Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity
Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity Open
Purpose The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) c…
View article: Complete topological asymptotic expansion for $L_2$ and $H^1$ tracking-type cost functionals in dimension two and three
Complete topological asymptotic expansion for $L_2$ and $H^1$ tracking-type cost functionals in dimension two and three Open
In this paper, we study the topological asymptotic expansion of a topology optimisation problem that is constrained by the Poisson equation with the design/shape variable entering through the right hand side. Using an averaged adjoint appr…
View article: Complete topological asymptotic expansion for $L_2$ and $H^1$\n tracking-type cost functionals in dimension two and three
Complete topological asymptotic expansion for $L_2$ and $H^1$\n tracking-type cost functionals in dimension two and three Open
In this paper, we study the topological asymptotic expansion of a topology\noptimisation problem that is constrained by the Poisson equation with the\ndesign/shape variable entering through the right hand side. Using an averaged\nadjoint a…
View article: Numerical shape optimization of the Canham-Helfrich-Evans bending energy
Numerical shape optimization of the Canham-Helfrich-Evans bending energy Open
In this paper we propose a novel numerical scheme for the Canham-Helfrich-Evans bending energy based on a three-field lifting procedure of the distributional shape operator to an auxiliary mean curvature field. Together with its energetic …
View article: Optimal Actuator Design for the Euler-Bernoulli Vibration Model Based on LQR Performance and Shape Calculus
Optimal Actuator Design for the Euler-Bernoulli Vibration Model Based on LQR Performance and Shape Calculus Open
A method for optimal actuator design in vibration control is presented. The optimal actuator, parametrized as a characteristic function, is found by means of the topological derivative of the LQR cost. An abstract framework is proposed bas…
View article: First-order differentiability properties of a class of equality constrained optimal value functions with applications
First-order differentiability properties of a class of equality constrained optimal value functions with applications Open
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to …
View article: Fully and semi-automated shape differentiation in NGSolve
Fully and semi-automated shape differentiation in NGSolve Open
View article: Asymptotic analysis and topological derivative for 3D quasi-linear magnetostatics
Asymptotic analysis and topological derivative for 3D quasi-linear magnetostatics Open
In this paper we study the asymptotic behaviour of the quasilinear curl - curl equation of 3D magnetostatics with respect to a singular perturbation of the differential operator and prove the existence of the topological derivative using a…
View article: Topological sensitivities via a Lagrangian approach for semilinear problems
Topological sensitivities via a Lagrangian approach for semilinear problems Open
In this paper we present a methodology that allows the efficient computation of the topological derivative for semilinear elliptic problems within the averaged adjoint Lagrangian framework. The generality of our approach should also allow …
View article: A shape optimization approach for electrical impedance tomography with point measurements
A shape optimization approach for electrical impedance tomography with point measurements Open
Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Gröger’s -e…
View article: Shape Optimization of Actuators over Banach Spaces for Nonlinear Systems
Shape Optimization of Actuators over Banach Spaces for Nonlinear Systems Open
In this paper, optimal actuator shape for nonlinear parabolic systems is discussed. The system under study is an abstract differential equation with a locally Lipschitz nonlinear part. A quadratic cost on the state and input of the system …
View article: A simplified derivation technique of topological derivatives for quasi-linear transmission problems
A simplified derivation technique of topological derivatives for quasi-linear transmission problems Open
In this paper we perform the rigorous derivation of the topological derivative for optimization problems constrained by a class of quasi-linear elliptic transmission problems. In the case of quasi-linear constraints, techniques using funda…
View article: A shape optimization approach for electrical impedance tomography with point measurements
A shape optimization approach for electrical impedance tomography with point measurements Open
Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Gr\"oger's $W^{1}_p…
View article: A shape optimization approach for electrical impedance tomography with pointwise measurements
A shape optimization approach for electrical impedance tomography with pointwise measurements Open
View article: Asymptotic analysis and topological derivative for 3D quasi-linear\n magnetostatics
Asymptotic analysis and topological derivative for 3D quasi-linear\n magnetostatics Open
In this paper we study the asymptotic behaviour of the quasilinear\n$curl$-$curl$ equation of 3D magnetostatics with respect to a singular\nperturbation of the differential operator and prove the existence of the\ntopological derivative us…