Greedy algorithms for eigenvalue optimization problems in shape design of two-density inhomogeneous materials.
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.
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ABSTRACT: this article we shall develop an algorithm for theSince its inception, the method has been used to computemotion of multiple junctions which is associated with anand analyze an array of mathematical and physical pheenergyfunctional involving the length of each interfacenomena. See, e.g.,  and the references theorem.and the area of each subregion. (Three-dimensional anaInearlier work , Merriman, Bence, and Osher havelogues are also easy to implement---the word "area" reextendedthe ...Journal of Computational Physics 08/1996; 127(1). · 2.14 Impact Factor
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ABSTRACT: We maximize the first eigenfrequency, or a sum of the first ones, of a bounded domain occupied by two elastic materials with a volume constraint for the most rigid one. A relaxed formulation of this problem is introduced, which allows for composite materials as admissible designs. These composites are obtained by homogenization of fine mixtures of the two original materials. We prove a saddle-point theorem that permits to reduce the full (unknown) set of admissible composite designs to the smaller set of sequential laminates which is explicitly known. Although our relaxation theorem is valid only for two non-degenerate materials, we deduce from it a numerical algorithm for eigenfrequency optimization in the context of optimal shape design (i.e. when one of the two materials is void). As is the case with all homogenization methods, our algorithm can be seen as a topology optimizer. Numerical results are presented for various two- and three-dimensional problems.Computer Methods in Applied Mechanics and Engineering. 01/2001;
Article: Greedy T-colorings of graphs.[show abstract] [hide abstract]
ABSTRACT: This paper deals with greedy T-colorings of graphs, i.e. T-colorings produced by the greedy (or first-fit) algorithm. We study their parameters, such as the number of colors, the span, the edge span and the values of colors they use. In particular, we show that these T-colorings have three nice properties: (1) their span and edge span are equal; (2) the number of colors they use is independent of T; (3) the set of colors they use is a function of T and the number of colors used, only. As a result of these considerations we receive some necessary and sufficient conditions for a greedy T-coloring to be optimal. The paper ends with some considerations concerning greedy algorithms with color interchange.Discrete Mathematics. 01/2009; 309:1685-1690.