EMSolution applies the Newton-Raphson method to solve nonlinear problems. Here, I would like to set aside the method itself and discuss its relation to the convergence of the ICCG method.

It is meaningless to make the convergence condition of the inner ICCG method too strong when the nonlinear loop has not converged. For this reason, EMSolution modifies the convergence conditions of the ICCG method in relation to the nonlinear convergence. In most cases, the convergence of the ICCG method begins with a sudden decrease in the convergence error, followed by a slower convergence. If the nonlinear convergence is not good enough, the method will enter the next nonlinear loop without allowing the slow convergence of the ICCG method to take place. We believe this is the main reason why EMSolution was significantly faster than other softwares on SRC's magnetic head benchmark problem .^[29]