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We developed two algorithms for solving the nonlinear electromagnetic inversion problem in the Earth. To achieve a balance between efficiency and robustness, both algorithms employ the Gauss-Newton inversion method. Moreover, to speed up the inversion's computational time, the so-called optimal grid technique is utilized. The first algorithm uses a forward solver with a very coarse optimal grid to calculate the Jacobian matrix. Hence, in this scheme we employ two different sets of optimal grids. One set is used to compute the data mismatch to be minimized and the other set is used to construct the Jacobian matrix. In the second approach we use a fixed-point iteration process where the inverse kernel is approximated on a coarse optimal grid that does not significantly compromise accuracy. The advantage of these optimal grids is that they considerably reduce the computation time without compromising accuracy. Numerical examples for two-dimensional axially symmetric and three-dimensional anisotropic configurations are used to demonstrate the advantage of using both algorithms over the standard Gauss-Newton inversion method.