Iterative methods for solving linear systems
Iterative methods for solving linear systems
An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
Mathematics of Computation
A justification of eddy currents model for the Maxwell equations
SIAM Journal on Applied Mathematics
Symmetric Coupling for Eddy Current Problems
SIAM Journal on Numerical Analysis
A Finite Element Method with Lagrange Multipliers for Low-Frequency Harmonic Maxwell Equations
SIAM Journal on Numerical Analysis
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In this paper, we study a time-dependent eddy current problem posed in the whole space. We prove that the problem has a well-posed weak formulation. We also show that the latter formulation admits a well-posed saddle point structure when the constraint satisfied by the magnetic field in the dielectric medium is handled by means of a Lagrange multiplier. Furthermore, we provide a BEM-FEM formulation of the problem that leads to a semi-discrete Galerkin scheme based on Nedelec's edge elements and Raviart-Thomas elements. Finally, we analyze the asymptotic behavior of the error in terms of the mesh size parameter.