We introduce MoVFEM, a computational algorithm for the modeling of three-dimensional magnetotelluric (MT) data using a vector finite element method of specific order from multiple elements' orders. Our algorithm allows complex geometries, topography, and anisotropic resistivity structures. The software calculates secondary electric and magnetic fields for a plane-wave primary magnetic field. Accurate calculation of fields in the boundary regions of the computational domain are ensured by the implementation of the Generalized Perfect Matched Layers method. We validate the MoVFEM algorithm by applications to various scenarios, which allow a comparison with analytical or accepted numerical solutions where available. The respective results of our algorithm are in good agreement with existing solutions. which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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A new numerical approach, called the "subdomain Chebyshev spectral method" is presented for calculation of the spatial derivatives in a curved coordinate system, which may be employed for numerical solutions of partial differential equations defined in a 2D or 3D geological model. The new approach refers to a "strong version" against the "weak version" of the subspace spectral method based on the variational principle or Galerkin's weighting scheme. We incorporate local nonlinear transformations and global spline interpolations in a curved coordinate system and make the discrete grid exactly matches geometry of the model so that it is achieved to convert the global domain into subdomains and apply Chebyshev points to locally sampling physical quantities and globally computing the spatial derivatives. This new approach not only remains exponential convergence of the standard spectral method in subdomains, but also yields a sparse assembled matrix when applied for the global domain simulations. We conducted 2D and 3D synthetic experiments and compared accuracies of the numerical differentiations with traditional finite difference approaches. The results show that as the points of differentiation vector are larger than five, the subdomain Chebyshev spectral method significantly improve the accuracies of the finite difference approaches.

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