Topology optimization searches for an optimal distribution of material and void without any restrictions on the structure of the design geometry. Shape optimization tunes the shape of the geometry, while the topology is fixed. In this paper we proceed sequentially with the optimal topology and shape design so that a coarsely optimized topology is the initial guess for the following shape optimi...

The paper deals with an efficient solution technique to large– scale discretized shape and topology optimization problems. The efficiency relies on multigrid preconditioning. In case of shape optimization, we apply a geometric multigrid preconditioner to eliminate the underlying state equation while the outer optimization loop is the sequential quadratic programming, which is done in the multil...

We prove a discrete version of the first Weber inequality on three-dimensional hybrid spaces spanned by vectors polynomials attached to elements and faces polyhedral mesh. then introduce two Hybrid High-Order methods for approximation magnetostatics model, in both its (first-order) field (second-order) vector potential formulations. These are applicable general meshes, allow arbitrary orders ap...

The use of algebraic formulation for the solution of electromagnetic fields is becoming more and more widespread. This paper presents the theoretical development of two algebraic formulations of the magneto-static problem and their implementation in a three dimensional computational procedure based on an unstructured tetrahedral mesh. A complete description of the variables used and of the solu...

The electromagnetic fields generated by a ring current around a Kerr black hole have been found. The acceleration of a charged particle by a force electric field along the rotation axis is investigated in the constructed model, as applied to the astrophysics of quasars.

High-field magnets of up to tens of teslas in strength advance applications in physics, chemistry and the life sciences. However, progress in generating such high fields has not been matched by corresponding advances in magnetic field measurement. Based mostly on nuclear magnetic resonance, dynamic high-field magnetometry is currently limited to resolutions in the nanotesla range. Here we repor...