The solution of Maxwell’s equations in multiphysics

•The solution of the fully-coupled equations of electromagnetics with fluid flows and structures is considered.•The electromagnetic effects are governed by the general Maxwell’s equations.•An effective finite element formulation for the solution of the Maxwell’s equations is presented.•The electric field and magnetic field intensities, or the electric and magnetic potentials, can be used.•Various example solutions are given that illustrate the use of the solution procedure.

We consider the solution of the fully-coupled equations of electromagnetics with fluid flows and structures. The electromagnetic effects are governed by the general Maxwell’s equations, the fluid flows by the Navier–Stokes equations, and the solids and structures by the general Cauchy equations of motion. We present an effective general finite element formulation for the solution of the Maxwell’s equations and demonstrate the coupling to the equations for fluids and structures. For the solution, we can use the electric field and magnetic field intensities, or the electric and magnetic potentials, with advantages depending on the problem solved. We give various example solutions that illustrate the use of the solution procedure.