Ana Alonso Rodríguez

A formulation of the eddy current problem in the presence of electric ports

The time-harmonic eddy current problem with either voltage or current intensity excitation is considered. We propose and analyze a new finite element approximation of the problem, based on a weak formulation where the main unknowns are the electric field in the conductor, a scalar magnetic potential in the insulator and, for the voltage excitation problem, the current intensity. The finite element approximation uses edge elements for the electric field and nodal elements for the scalar magnetic potential, and an optimal error estimate is proved. Some numerical results illustrating the performance of the method are also presented.

Construction of a Finite Element Basis of the First de Rham Cohomology Group and Numerical Solution of 3D Magnetostatic Problems

We devise an efficient algorithm for the finite element approximation of harmonic fields and the numerical solution of three-dimensional magnetostatic problems. In particular, we construct a finite element basis of the first de Rham cohomology group of the computational domain. The proposed method works for general topological configurations and does not need the determination of “cutting” surfaces.

Inverse source problems for eddy current equations

We study the inverse source problem for the eddy current approximation of Maxwell equations. As for the full system of Maxwell equations, we show that a volume current source cannot be uniquely identified by knowledge of the tangential components of the electromagnetic fields on the boundary, and we characterize the space of non-radiating sources. On the other hand, we prove that the inverse source problem has a unique solution if the source is supported on the boundary of a subdomain or if it is the sum of a finite number of dipoles. We address the applicability of this result for the localization of brain activity from electroencephalography and magnetoencephalography measurements.

Iterative methods for the saddle-point problem arising from the HC /EI formulation of the eddy current problem

This paper is concerned with the solution of the linear system arising from a finite element approximation of the time-harmonic eddy current problem. We consider the

Efficient Construction of 2-Chains with a Prescribed Boundary

{\bf H}_C/{\bf E}_I

Finite element simulation of eddy current problems using magnetic scalar potentials

formulation introduced and analyzed in [A. M. Alonso Rodriguez, R. Hiptmair, and A. Valli, Numer. Methods Partial Differential Equations, 21 (2005), pp. 742–763], where an optimal error estimate for the finite element approximation using edge elements of the first order is proved. Now we propose and analyze iterative procedures for the solution of the resulting linear system based on the physical decomposition of the computational domain in an insulating region and a conducting one. If the insulator does not contain any nonbounding cycle, we prove that the Dirichlet–Neumann iteration converges with a rate that is independent of the mesh size. In the case of a connected conductor with general topology we propose to use either a modified version of the Dirichlet–Neumann iteration or an Uzawa-like method. We compare the per...

A posteriori error estimates for the problem of electrostatics with a dipole source

Let

Coupling DG-FEM and BEM for a Time Harmonic Eddy Current Problem

\Omega

Existence and uniqueness of the solution

be a bounded domain of

Setting the problem

{\mathbb R}^3