通过浅水方程减轻海岸侵蚀的形状Optimization
Shape Optimization for the Mitigation of Coastal Erosion via Shallow Water Equations
摘要：
海岸侵蚀描述了破坏性的海浪、海流或潮汐造成的陆地位移。为了减轻这些影响，人们做出了很大努力，使用了丁坝、防波堤和各种其他结构。我们试图解决这个问题，通过应用形状优化技术的障碍。我们使用二维浅水方程模拟波浪向海岸线的传播。障碍物的形状是在一个适当的费用函数优化，以尽量减少沿海岸的水波的高度和速度，不依赖于一个有限维的设计空间，但基于形状演算。
英文摘要：
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.
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