A new external velocity field for active contours is proposed. The velocity field is based on magnetostatics and hypothesised magnetic interactions between the active contour and image gradients. In this paper, we introduce the method and study its convergence capability for the recovery of shapes with complex topology and geometry, including deep, narrow concavities. The proposed active contou...

Abstract Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge ...

This review describes the composition of Compact Muon Solenoid (CMS) detector and methodology for modelling heterogeneous CMS magnetic system, starting with formulation magnetostatics problem flux superconducting solenoid enclosed in a steel flux-return yoke. The includes section on magnetization curves various types used magnet evolution system model over 20 years is presented discussion well ...

In this paper we study the asymptotic behaviour of quasilinear curl - equation 3D magnetostatics with respect to a singular perturbation differential operator and prove existence topological derivative using Lagrangian approach. We follow strategy proposed in Gangl Sturm ( ESAIM: COCV 26 (2020) 106) where systematic concise way for derivation derivatives quasi-linear elliptic problems H 1 is in...

The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to smooth the rotation pattern of the rotor. A shape optimization problem is formulated by introducing a tracking-type cost functional to match a desired rotation pattern. The magnetic field generated by perman...

We review the use of block diagonal and block lower/upper triangular splittings for constructing iterative methods and preconditioners for solving stabilized saddle point problems. We introduce new variants of these splittings and obtain new results on the convergence of the associated stationary iterations and new bounds on the eigenvalues of the corresponding preconditioned matrices. We furth...