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

TL;DR

This paper applies shape optimization techniques to the Helmholtz equation to design coastal structures that reduce wave impact and mitigate erosion, using shape calculus without predefined design spaces.

Contribution

It introduces a novel shape optimization approach for wave mitigation based on the Helmholtz equation and shape calculus, avoiding finite-dimensional design restrictions.

Findings

Optimized obstacle shapes reduce wave height along coastlines.

Shape calculus effectively guides shape modifications for erosion mitigation.

Method provides a flexible framework for coastal structure design.

Abstract

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.