TY - JOUR
T1 - Variational Formulation for Maxwell's Equations with Lorenz Gauge: Existence  and Uniqueness of Solution
AU - Michal Kordy, Elena Cherkaev & Phil Wannamaker
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 731
EP - 749
PY - 2015
DA - 2015/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/509.html
KW - Lorenz gauge, Schelkunoff potential, Maxwell's equations, Finite Element Method, Nodal shape functions, Regularization.
AB - <p style="text-align: justify;">The existence and uniqueness of a vector scalar potential representation with the
Lorenz gauge (Schelkunoff potential) is proven for any vector field from H(curl). This representation
holds for electric and magnetic fields in the case of a piecewise smooth conductivity,
permittivity and permeability, for any frequency. A regularized formulation for the magnetic field
is obtained for the case when the magnetic permeability&nbsp;$\mu$ is constant and thus the magnetic field
is divergence free. In the case of a non divergence free electric field, an equation involving scalar
and vector potentials is proposed. The solution to both electric and magnetic formulations may
be approximated by the nodal shape functions in the finite element method with system matrices
that remain well-conditioned for low frequencies. A numerical study of a forward problem of a
computation of electromagnetic fields in the diffusive electromagnetic regime shows the efficiency
of the proposed method.</p>