TY - JOUR A1 - Günnel, Andreas A1 - Herzog, Roland T1 - Optimal Control Problems in Finite-Strain Elasticity by Inner Pressure and Fiber Tension JF - Frontiers in Applied Mathematics and Statistics N2 - 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. KW - partial differential equations, optimal control, finite-strain elasticity, quasi-Newton method, multigrid preconditioning Y1 - 2016 U6 - https://doi.org/10.3389/fams.2016.00004 VL - 2 ER - TY - JOUR A1 - Andreas, Günnel A1 - Herzog, Roland A1 - Sachs, Ekkehard T1 - A Note on Preconditioners and Scalar Products in Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space JF - Electronic Transactions on Numerical Analysis N2 - 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. KW - Krylov subspace methods, preconditioners, scalar products, Hilbert spaces, Riesz isomorphism Y1 - 2014 UR - https://etna.ricam.oeaw.ac.at/vol.41.2014/pp13-20.dir/pp13-20.pdf VL - 2014 IS - 41 SP - 13 EP - 20 ER - TY - JOUR A1 - Makowski, Andreas A1 - Herzog, Roland T1 - Optimal Control of Large Deformation Elasticity by Fiber Tension JF - Proceedings in Applied Mathematics and Mechanics N2 - 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. KW - partial differential equations, optimal control, finite-strain elasticity, quasi-Newton method, multigrid preconditioning Y1 - 2014 U6 - https://doi.org/10.1002/pamm.201410420 VL - 2014 IS - 14 SP - 879 EP - 880 ER -