A Monotonic Algorithm for Eigenvalue Optimization in Shape Design Problems of Multi-Density Inhomogeneous Materials
Year: 2010
Communications in Computational Physics, Vol. 8 (2010), Iss. 3 : pp. 565–584
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.190309.201009a
Communications in Computational Physics, Vol. 8 (2010), Iss. 3 : pp. 565–584
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20