# Alternative formulation of Maxwell equation

Hi everybody,

I wonder, is it possible to apply bempp to solve Maxwell equation in alternative formulation I found in article “Overcoming Low-Frequency Breakdown of the Magnetic Field Integral Equation” https://doi.org/10.1109/TAP.2012.2230232

The idea is to calculate current J on surface \Gamma from the tangential boundary condition on the magnetic field

J - n \times H = n \times H^{inc}

which is second kind Fredholm equation and free of “low-frequency breakdown”. Here n is external normal vector, H^{inc} is incident magnetic field, H is unknown magnetic field, induces by current J,

H(x) = \nabla \times \int_\Gamma g_k(x-y) J(y) dA_y

g_k is Green function for scalar Helmholtz equation.

The magnetic field integral equation to solve is

\frac{1}{2} J(x) - n(x) \times \nabla \times \int_\Gamma g_k(x - y) J(y) dA_y = n(x) \times H^{inc}(x) \quad (x \in \Gamma)

It it possible to apply n \times operator to magnetic field operator befor summation with identity operator?

Hope for you support.

Hi, not sure I understand you correctly. But magnetic field integral equations are no problem. See the paper here: Software frameworks for integral equations in electromagnetic scattering based on Calderón identities - ScienceDirect