Finite difference modeling of global geomagnetic induction using finite-difference methods on nested quasi-regular triangular grids.

A new numerical algorithm is presented for modeling and simulation of global-scale geomagnetic induction phenomena. The difficulty of modeling induction fields over a spherical body is closely tied to the compromise between discretization complexity, and the complexity of numerical solution for solving the governing partial differential equations. For example, while finite element technique offers great flexibility in the discretization of the underlying Earth model, accurate solutions often require the use of exotic basis functions or the introduction of some combination of potentials which are later differentiated to obtain the fields of interest. Alternatively, finite difference solutions have been derived directly in terms of the observable fields, however, with that caveat that excessive detail and computational effort is expended near the poles of the Earth owing to the convergence of longitude lines in the underlying tensor-product grid. As a compromise between these two methods, a finite-difference solution is presented here which solves directly for the frequency domain magnetic fields throughout the conducting Earth and above, into the near-space region, based on a discretization of triangulated, nested spherical shells. The flux-conserving finite difference stencil is constructed from the integral form of Maxwell's equations and source terms are represented by a truncated spherical harmonic expansion for either internal or external time--varying Gauss coefficients. Numerical experiments demonstrate good agreement with known analytic solutions. Applications in satellite-- and/or ground--based geomagnetic field analysis are considered.