@article{GuennelHerzog, author = {G{\"u}nnel, Andreas and Herzog, Roland}, title = {Optimal Control Problems in Finite-Strain Elasticity by Inner Pressure and Fiber Tension}, series = {Frontiers in Applied Mathematics and Statistics}, volume = {2}, journal = {Frontiers in Applied Mathematics and Statistics}, doi = {10.3389/fams.2016.00004}, abstract = {Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance.}, language = {en} } @article{AndreasHerzogSachs, author = {Andreas, G{\"u}nnel and Herzog, Roland and Sachs, Ekkehard}, title = {A Note on Preconditioners and Scalar Products in Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space}, series = {Electronic Transactions on Numerical Analysis}, volume = {2014}, journal = {Electronic Transactions on Numerical Analysis}, number = {41}, pages = {13 -- 20}, abstract = {The conjugate gradient and minimal residual methods for the solution of linear systems Ax = b are considered. The operator A is bounded and self-adjoint and maps a Hilbert space X into its dual X∗. This setting is natural for variational problems such as those involving linear partial differential equations. The derivation of the two methods in Hilbert spaces shows that the choice of a preconditioner is equivalent to the choice of the scalar product in X.}, language = {en} } @article{MakowskiHerzog, author = {Makowski, Andreas and Herzog, Roland}, title = {Optimal Control of Large Deformation Elasticity by Fiber Tension}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {2014}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {14}, doi = {10.1002/pamm.201410420}, pages = {879 -- 880}, abstract = {Object of our interest is an elastic body Ω ⊂ ℝ3 which we can deform by applying a tension along certain given short fibers inside the body. The deformation of the body is desribed by a hyperelastic model with polyconvex energy density and a special energy functional for the tension along the fibers. We seek to apply (possibly large) deformations to the body so that a desired shape is obtained. To this end, we formulate an optimal control problem for the fiber tension field.}, language = {en} }