# Ke-wei Liang

Zhejiang University, Hang-hsien, Zhejiang Sheng, China

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## Publications (2)2.77 Total impact

• ##### Article: Greedy algorithms for eigenvalue optimization problems in shape design of two-density inhomogeneous materials
Zheng-Fang Zhang · Ke-Wei Liang · Xiao-Liang Cheng
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ABSTRACT: This paper studies the eigenvalue optimization problems in the shape design of the two-density inhomogeneous materials. Two types of greedy algorithms are proposed to solve three optimization problems in finite element discretization. In the first type, the whole domain is initialized by one density. For each problem of the eigenvalue optimizations, we define a measurement of the element, which is the criterion to determine the ‘best’ element. We change the density of the ‘best’ element to the other density. Then the algorithm repeats the procedure until the area constraint is satisfied. In the second type, the algorithm begins with the density distribution satisfying the area constraint. Also, according to the measurement of the element, the algorithm finds a pair of the ‘best’ elements and exchanges their densities between each other. Furthermore, the accelerating greedy algorithms are proposed to speed up both two types. Three numerical examples are provided to illustrate the results.
No preview · Article · Jan 2011 · International Journal of Computer Mathematics
• ##### Article: A Monotonic Algorithm for Eigenvalue Optimization in Shape Design Problems of Multi-Density Inhomogeneous Materials
Zheng-fang Zhang · Ke-wei Liang · Xiao-liang Cheng
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ABSTRACT: Many problems in engineering shape design involve eigenvalue optimizations. The relevant difficulty is that the eigenvalues are not continuously differentiable with respect to the density. In this paper, we are interested in the case of multi-density inhomogeneous materials which minimizes the least eigenvalue. With the finite element discretization, we propose a monotonically decreasing algorithm to solve the minimization problem. Some numerical examples are provided to illustrate the efficiency of the present algorithm as well as to demonstrate its availability for the case of more than two densities. As the computations are sensitive to the choice of the discretization mesh sizes, we adopt the refined mesh strategy, whose mesh grids are 25-times of the amount used in [S. Osher and F. Santosa, J. Comput. Phys., 171 (2001), pp. 272-288]. We also show the significant reduction in computational cost with the fast convergence of this algorithm.
No preview · Article · Sep 2010 · Communications in Computational Physics

#### Publication Stats

 10 Citations 2.77 Total Impact Points

#### Institutions

• ###### Zhejiang University
• Department of Mathematics
Hang-hsien, Zhejiang Sheng, China