TY - JOUR
T1 - A Monotonic Algorithm for Eigenvalue Optimization in Shape Design Problems of Multi-Density Inhomogeneous Materials
AU - Zheng-fang Zhang, Ke-wei Liang & Xiao-liang Cheng
JO - Communications in Computational Physics
VL - 3
SP - 565
EP - 584
PY - 2010
DA - 2010/08
SN - 8
DO - http://doi.org/10.4208/cicp.190309.201009a
UR - https://global-sci.org/intro/article_detail/cicp/7585.html
KW - 
AB - <p style="text-align: justify;">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.</p>