In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The parametrization enters through geometry of domain and thus, combined nonlinearity, drives our reduction problem. We provide residual-based a-posteriori error bo...

Biomimetic micro-swimmers can be used for various medical applications, such as targeted drug delivery and micro-object (e.g. biological cells) manipulation, in lab-on-a-chip devices. Bacteria swim using a bundle of flagella (flexible hair-like structures) that form a rotating cork-screw of chiral shape. To mimic bacterial swimming, we employ a computational approach to design a bacterial (chir...

Optimization and inverse problems governed with partial differential equations are often formulated as constrained nonlinear programming problems via the Lagrange formalism. The nonlinearity is treated using the sequential quadratic programming. A numerical solution then hinges on an efficient iterative method for the resulting saddle–point systems. In this paper we apply a semi–monotonic augme...

Magnetic domains play a fundamental role in magnetization processes. However, unlike ferromagnets (FMs), the formation of antiferromagnets (AFMs) is poorly understood because they are not favored by magnetostatics and difficult to detect experimentally. In this paper, we create synthetic planar AFM with tunable lateral coupling between neighboring FM regions establish played magnetic disorder d...

Density-based topology optimization (TO) methodologies in magnetostatics interpolate either the magnetic permeability $\mu $ or reluctivity notation="LaTeX">$\nu to define intermediate materials and compute problem sensitivities. Thes...

We present a numerical method for the solution of three-dimensional linear magnetostatic problems by embedding their geometry into symmetric domain and Fourier expansion in symmetry coordinate, leading to set decoupled two-dimensional problems. Special cases include axial translational symmetry. To keep treatment universal, framework decomposition vector potential formulation is developed covar...