Implementation and Validation of the Dual Full-Wave E and H Formulations with Electric Circuit Element Boundary Conditions

Dual full-wave (FW) frequency-domain \(\textbf{E}\) and \(\textbf{H}\) formulations, with scalar potentials on the boundary, and with electric circuit element boundary conditions are discussed and details about their implementation in the finite element method are given. For some magneto-quasi-static devices this duality frames the exact solution thus allowing the accuracy control. In such cases the geometric mean of the dual solutions exhibits a better accuracy and higher convergence rate than the individual numerical solutions. For FW devices the dual formulations allow a compromise between model accuracy and computational effort, especially if the models are not 3D. Implementation is available for free in onelab. Validation for test cases with analytic solution are provided: a conducting cylinder and a coaxial cable.