A note on Ricci flow and optimal transportation
We describe a new link between Perelman’s monotonicity formula for the reduced volume and ideas from optimal transport theory.
A Note on the Interpretation of Closed H-Surfaces in Physical Terms.
A note on weak approximation of minors
A notion of total variation depending on a metric with discontinuous coefficients
A parametric variational principle for minimal surfaces of varying topological type.
A penalty method for topology optimization subject to a pointwise state constraint
This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.
A Pertubation Theorem for Surfaces of Constant Mean Curvature.
A phase-field model for compliance shape optimization in nonlinear elasticity
Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...
A phase-field model for compliance shape optimization in nonlinear elasticity
Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...
A phase-field model for compliance shape optimization in nonlinear elasticity
Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the...
A priori error estimates for finite element discretizations of a shape optimization problem
In this paper we consider a model shape optimization problem. The state variable solves an elliptic equation on a domain with one part of the boundary described as the graph of a control function. We prove higher regularity of the control and develop a priori error analysis for the finite element discretization of the shape optimization problem under consideration. The derived a priori error estimates are illustrated on two numerical examples.
A Priori estimates for minimal surfaces with free boundary, which are not minima of the area.
A quantitative isoperimetric inequality in n-dimensional space.
A “quasi maximum principle” for -surfaces
A refined Newton’s mesh independence principle for a class of optimal shape design problems
Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.
A regularity theorem for curvature flows.
A regularized Newton method in electrical impedance tomography using shape Hessian information
A relaxation result for energies defined on pairs set-function and applications
We consider, in an open subset Ω of , energies depending on the perimeter of a subset (or some equivalent surface integral) and on a function u which is defined only on . We compute the lower semicontinuous envelope of such energies. This relaxation has to take into account the fact that in the limit, the “holes” E may collapse into a discontinuity of u, whose surface will be counted twice in the relaxed energy. We discuss some situations where such energies appear, and give, as an application,...
A relaxation theorem in the space of functions of bounded deformation
A remark about minimal surfaces with flat embedded ends.