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Discrete Gradient Flows for Shape Optimization and Applications
Shape optimization scalar product gradient flow
2015/12/11
We present a variational framework for shape optimization problems
that establishes clear and explicit connections among the continuous formulation, its full discretization and the resulting linear a...
In this study, shape optimisation of cantilever beams has been carried out using neural network. Considering different geometrical parameters, finite element analyses of cantilever beams are carried o...
Shape Optimization Problems over Classes of Convex Domains
Shape Optimization Problems Convex Domains
2009/2/5
We consider shape optimization problems of the form
\min\left\{\int_{\partial A} f(x,\nu(x))\hbox{d}x {\cal{H}^{n-1}} :A\in{\cal A}\right\}
where $f$ is any continuous function and the class ${\ca...
Lipschitz Continuity of the State Function in a Shape Optimization Problem
Lipschitz State Function Optimization Problem
2009/1/20
This paper deals with the existence and the regularity of state function $u$ in an $N$-dimensional shape optimization problem. We use a variational approach to get the existence of a solution $u$ of a...