arXiv subjects

Luka Schlegel

Publications and source records attributed to Luka Schlegel.

5 recordsLinked to original sources

arXiv2026

A Probabilistic Approach to Shape Derivatives

We introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for second-order semilinear elliptic PDEs with Dirichlet boundary conditions and a general class of target functions. The probabilistic representation derives from an extension of a boundary sensitivity result for diffusion processes due to Costantini, Gobet and El Karoui [14]. Moreover, we present a simulation methodology based on our results that does not necessarily require a mesh of the relevant domain, and provide Taylor tests to verify its numerical accuracy

math.OC↗

arXiv2022

Shape Optimization for the Mitigation of Coastal Erosion via Shallow Water Equations

Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Major efforts have been made to mitigate these effects using groins, breakwaters and various other structures. We try to address this problem by applying shape optimization techniques to the obstacles. We model the propagation of waves towards the coastline, using two-dimensional shallow water equations. The obstacle's shape is optimized over an appropriate cost function to minimize the height and velocities of water waves along the shore, without relying on a finite-dimensional design space but based on shape calculus.

math.OC↗

arXiv2022

Shape Optimization for the Mitigation of Coastal Erosion via Smoothed Particle Hydrodynamics

Adjoint-based shape optimization most often relies on Eulerian flow field formulations. However, since Lagrangian particle methods are the natural choice for solving sedimentation problems in oceanography, extensions to the Lagrangian framework are desirable. For the mitigation of coastal erosion, we perform shape optimization for fluid flows, that are described by Lagrangian shallow water equations and discretized via smoothed particle hydrodynamics. The obstacle's shape is hereby optimized over an appropriate cost function to minimize the height of water waves along the shoreline based on shape calculus. Theoretical results will be numerically verified by exploring different scenarios.

physics.flu-dyn↗

arXiv2022

Shape Optimization for the Mitigation of Coastal Erosion via Porous Shallow Water Equations

Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Major efforts have been made to mitigate these effects using groynes, breakwaters and various other structures. We address this problem by applying shape optimization techniques on the obstacles. We model the propagation of waves towards the coastline using two-dimensional porous Shallow Water Equations with artificial viscosity. The obstacle's shape, which is assumed to be permeable, is optimized over an appropriate cost function to minimize the height and velocities of water waves along the shore, without relying on a finite-dimensional design space, but based on shape calculus.

math.OC↗

arXiv2022

Shape Optimization for the Mitigation of Coastal Erosion via the Helmholtz Equation

Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Major efforts have been made to mitigate these effects using groins, breakwaters and various other structures. We try to address this problem by applying shape optimization techniques on the obstacles. A first approach models the propagation of waves towards the coastline, using a 2D time-harmonic system based on the famous Helmholtz equation in the form of a scattering problem. The obstacle's shape is optimized over an appropriate cost function to minimize the height of water waves along the shoreline, without relying on a finite-dimensional design space, but based on shape calculus.

math.OC↗