Related papers: A Reduced Magnetic Vector Potential Approach with …
We introduce a formulation where individual line segments of a current loop have translationally non-invariant contributions to the electro-quasi-static magnetic scalar potential and magnetic field in source-free regions. While closed…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
The magnetostatic field distribution in a nonlinear medium amounts to the unique minimizer of the magnetic coenergy over all fields that can be generated by the same current. This is a nonlinear saddlepoint problem whose numerical solution…
This contribution combines a low-rank matrix approximation through Singular Value Decomposition (SVD) with second-order Krylov subspace-based Model Order Reduction (MOR), in order to efficiently propagate input uncertainties through a given…
We describe a compatible finite element discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity…
The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorsky-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The method is based on a bilevel optimization problem, where the…
We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. Both methods employ the $H_{\rm div}$ conforming BDM element coupled with an…
Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization.…
This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
We show that the equations satisfied by weakly quasisymmetric magnetic fields can be solved to arbitrarily high order in powers of the distance from the magnetic axis. This demonstration does not consider force balance. The existence of…
This work deals with shape optimization of electric machines using isogeometric analysis. Isogeometric analysis is particularly well suited for shape optimization as it allows to easily modify the geometry without remeshing the domain. A…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
Hybrid magnetic shields with both active field generating components and high-permeability magnetic shielding are increasingly needed for a variety of technologies and experiments that require precision-controlled magnetic field…
Finite-element simulations of magnetostatic fields are performed in terms of magnetic vector and total scalar potentials and compared for purpose of modeling the accelerator magnets. The potentials represent the unknown variables associated…
This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework,…