Shape Optimization for Mitigating Coastal Erosion

海岸侵蚀是一种自然现象，全球变暖加剧了这一现象，对塞内加尔等拥有大片沿海地区的国家产生了重大的经济影响。本项目旨在建立一个理论和数值框架，以稳健地处理减缓海岸侵蚀的形状和拓扑优化问题。在海岸侵蚀的背景下，形状和拓扑优化问题的问题类别是新的，因此提出了特殊的挑战：典型的潮汐效应模型依赖于无渐近分析，往往面向模拟而不是面向优化，并且操作优化目标的适当数学公式是开放的。因此，这个项目是基础性的，将提供初步的见解，进一步的探索步骤可以建立在此基础上。因此，我们的主要项目目标如下：-分析适当的系统模型。-合理制定优化目标。-研究解的存在性和适定性。-制定具体问题的算法方法。-优化策略的鲁棒化。-概念和具体最优解的表征和计算。

Coastal erosion is a natural phenomenon, exacerbated by global warming, which has significant economic impact on countries with a large coastal part, like Senegal.This project aims at establishing a theoretical and numerical framework for the robust treat- ment of shape and topology optimization problems for the mitigation of coastal erosion. The problem class of shape and topology optimization problems in the context of coastal erosion is new and thus poses particular challenges: typical models for tidal effects rely on asymp- totic analysis often geared towards simulation but not towards optimization, and the proper mathematical formulation of operational optimization goals is open.Thus, this project is of fundamental nature and will provide first insights, onto which further exploration steps can be built on. Therefore, we aim at the following major project goals:- Analysis of proper system models. - Proper formulation of optimization objectives. - Study of existence of solutions and well-posedness. - Formulation of problem specific algorithmic approaches.- Robustification of optimization strategies. - Characterization and computation of conceptual and specific optimal solutions.