A Variational Binary Level Set Method for Structural Topology Optimization

This paper proposes a variational binary level set method for shape and topology optimization of structural.First,a topology optimization problem is presented based on the level set method and an algorithm based on binary level set method is proposed to solve such problem.Considering the difficulties of coordination between the various parameters and efficient implementation of the proposed method,we present a fast algorithm by reducing several parameters to only one parameter,which would substantially reduce the complexity of computation and make it easily and quickly to get the optimal solution.The algorithm we constructed does not need to re-initialize and can produce many new holes automatically.Furthermore,the fast algorithm allows us to avoid the update of Lagrange multiplier and easily deal with constraints,such as piecewise constant,volume and length of the interfaces.Finally,we show several optimum design examples to confirm the validity and efficiency of our method.

Fractal geometry and topology abstracted from hair fibers

Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2）-circle fractal sets as subsets. As far as the （9＋2） topological patterns are concerned, the following propositions are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.

Binary Level Set Methods for Dynamic Reservoir Characterization by Operator Splitting Scheme

In this paper,operator splitting scheme for dynamic reservoir characterization by binary level set method is employed.For this problem,the absolute permeability of the two-phase porous medium flow can be simulated by the constrained augmented Lagrangian optimization method with well data and seismic time-lapse data.By transforming the constrained optimization problem in an unconstrained one,the saddle point problem can be solved by Uzawas algorithms with operator splitting scheme,which is based on the essence of binary level set method.Both the simple and complicated numerical examples demonstrate that the given algorithms are stable and efficient and the absolute permeability can be satisfactorily recovered.