Optimal Shape Design for the p-Laplacian Eigenvalue Problem
Optimal Shape Design for the p-Laplacian Eigenvalue Problem
复制标题
p-拉普拉斯特征值问题的最优形状设计
DOI：
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发表时间：
2018
影响因子：
2.5
通讯作者：
H. Voss
中科院分区：
文献类型：
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作者：
S. Mohammadi;Farid Bozorgnia;H. Voss
本文研究了一类与p-拉普拉斯算子相对应的形状优化问题。给定一个由阶跃函数生成的重排类中的密度函数，求出使主特征值尽可能小的密度。考虑由两种不同材料组成的已知固定质量和规定形状的固定边界的膜，我们的结果确定了这些材料的分布方式，使膜的基本频率最小。我们获得了优化器的一些定性方面，然后我们确定了近最优集，这是对特定参数值范围的最小化器的近似值。提出了一种求最优形状的数值算法，并证明了该算法收敛于局部极小值。最后给出了不同领域的数值实例，说明了该方法的有效性和实用性。
In this paper, a shape optimization problem corresponding to the p-Laplacian operator is studied. Given a density function in a rearrangement class generated by a step function, find the density such that the principal eigenvalue is as small as possible. Considering a membrane of known fixed mass and with fixed boundary of prescribed shape consisting of two different materials, our results determine the way to distribute these materials such that the basic frequency of the membrane is minimal. We obtain some qualitative aspects of the optimizer and then we determine nearly optimal sets which are approximations of the minimizer for specific ranges of parameters values. A numerical algorithm is proposed to derive the optimal shape and it is proved that the numerical procedure converges to a local minimizer. Numerical illustrations are provided for different domains to show the efficiency and practical suitability of our approach.
权重不定的拟线性椭圆诺伊曼问题的特征值最小化
影响因子：
1.3
作者：
A. Derlet;J.-P. Gossez;P. Takac
通讯作者：
P. Takac