Reduction of computing time for steady-state solutions of magnetic field and circuit coupled problems using time-domain finite-element method

Time-stepping finite-element method (FEM) does not just analyze the transient process of magnetic fieldelectric circuitmechanical motion coupled problems, it can also be used to find their steady-state solutions. In this paper, four effective measures are proposed to significantly reduce the computing time for finding steady-state solutions. With the first measure, it is proposed that first-order elements be used to replace second-order elements before the solution reaches its steady-state. A simple method is also proposed to allow a computer program of second-order element FEM to be used for first-order element FEM. The second measure is to adjust the error tolerance of nonlinear iteration and, with the permeability of iron materials from the last step being used as the initial values at the beginning of each time step, the nonlinear iterations can either be avoided or the number of iterations reduced. The third measure proposes a modified one-step multistage diagonally-implicit Runge-Kutta (DIRK) algorithm. In the fourth measure, during the transient process in the run-up towards steady-state operation, the time step size of the time integration is gradually reduced to a normal value. Numerical experiment shows that the computing time required to reach steady-state, using the combined four proposed methods, is only about 11% of that required by using conventional method.