科研之友
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摘要
We consider to solve numerically the shape optimization problems of Dirichlet Laplace eigenvalues subject to volume and perimeter constraints. By combining a level set method with the relaxation approach, the algorithm can perform shape and topological changes on a fixed grid. We use the volume expressions of Eulerian derivatives in shape gradient descent algorithms. Finite element methods are used for discretizations. Two and three-dimensional numerical examples are presented to illustrate the effectiveness of the algorithms.
