论文标题
最小最大方法，形状，拓扑衍生物，平均拉格朗日，同质化，两个比例收敛，helmholtz方程
Min max method, shape, topological derivatives, averaged Lagrangian, homogenization, two scale convergence, Helmholtz equation
论文作者
论文摘要
在本文中，我们执行了严格的形状和拓扑导数，以在约束Helmoltz问题下进行优化问题。通过引入成本功能来提出形状和拓扑优化问题。我们首先通过考虑lagradian方法来得出功能的形状衍生物。它也被证明是一种具有相同方法的拓扑导数。还给出了差异几何形状引起的几个不受约束的形状函数的应用。
In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We derive first by considering the lagradian method the shape derivative of the functional. It is also proven a topological derivative with the same approach. An application to several unconstrained shape functions arising from differential geometry are also given.
