A nonlinear time-domain element differential method for solving two-dimensional electro- and magneto- quasistatic problems

The transient quasi-static electromagnetic problems with nonlinear conductive effects are under consideration in this paper. The quasi-static electromagnetic problems include electro-quasistatic (EQS) and magneto-quasistatic (MQS) problems, which neglect the wave propagation effects, and are important in the electrical engineering. Numerical computation is an efficient manner for solving these problems, apart from all the existing numerical methods, a new efficient nonlinear time-domain element differential method (TD-EDM) is presented to solve these problems in this paper. In the method, the governing equations and boundary conditions are directly solved in a strong form. The isoparametric elements are used to discrete the geometries, and the first- and second- order derivatives of the shape functions with respect to global coordinates are analytically derived. And the time derivatives of the basic variable are discretized by implicit Euler scheme. In order to handle the nonlinear effects induced by the nonlinear conductivities in the final system of equations, the Newton-Raphson iterative scheme is constructed to solve the nonlinear system of equations at each time step. Finally, several numerical examples are employed to validate the correctness of the proposed method.