Novel algorithm based on transmission-line modeling in the finite-element method for nonlinear quasi-static field analysis

Nonlinear quasi-static field problems are generally solved by means of the finite-element method coupled with some classical time-stepping technique, such as the Crank-Nicolson iterative scheme, for solution in the time domain. At each time step, the nonlinearity must be treated iteratively, and a new linear system must be solved every iteration, which is costly in terms of computation time. Here, a novel algorithm based on transmission-line modeling is proposed to deal both with the nonlinearity and solution in the time domain. The underlying idea is the analogy that exists between the finite-element matrix and the node-admittance matrix of an equivalent network where resistors and capacitors hold the material properties. The nonlinear material is replaced by a fictitious linear and homogeneous one, which permits a global stiffness matrix to remain unchanged throughout the iterative process. The emerging time-stepping scheme is precisely the same as the Crank-Nicolson scheme, and so is the accuracy. Two numerical examples demonstrate the efficiency of the method.