Related papers: Space-time shape optimization of rotating electric…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
We consider systems of nonlinear magnetostatics and quasistatics that typically arise in the modeling and simulation of electric machines. The nonlinear problems, eventually obtained after time discretization, are usually solved by…
In this work we study a general shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian-Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in…
Aerodynamic shape optimization has established itself as a valuable tool in the engineering design process to achieve highly efficient results. A central aspect for such approaches is the mapping from the design parameters which encode the…
We investigate the three-dimensional structure of the pulsar magnetosphere through time-dependent numerical simulations of a magnetic dipole that is set in rotation. We developed our own Eulerian finite difference time domain numerical…
Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi-static motions of…
Magnetic soft robots embedded with hard magnetic particles enable untethered actuation via external magnetic fields, offering remote, rapid, and precise control, which is highly promising for biomedical applications. However, designing such…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical…
The magnetization evolution of the free layer in an orthogonal spin-torque device is studied based on a macrospin model. The trajectory of magnetization vector under various conditions has shown rich nonlinear properties. The phase diagram…
In this work we conduct a numerical search of non-trivial mechanisms, leading to new tendencies towards long-range ferromagnetic ordering in two-dimensional materials. For this purpose we employ an original variant of pairwise infinitesimal…
Using the method of superbosonization we consider a model of a random magnetic field (RMF) acting on both orbital motion and spin of electrons in two dimensions. The method is based on exact integration over one particle degrees of freedom…
A variational time discretization of anisotropic Willmore flow combined with a spatial discretization via piecewise affine finite elements is presented. Here, both the energy and the metric underlying the gradient flow are anisotropic,…
Relativistic theory of the Cox's scalar not point-like particle with intrinsic structure is developed on the background of arbitrary curved space-time. It is shown that in the most general form, the extended Proca-like tensor first order…
The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'two-dimensional' version of…