On the self-consistent algorithm for numerical simulation of the global geomagnetic disturbances and associated electric current spreading to low latitudes

We present a finite elements algorithm (FEA) for study of the global current systems produced by extra low frequency electromagnetic disturbances like hydromagnetic waves, solar-quite daily variations, and so on. All these problems can be reduced to Laplace´s equation on a thin nonhomogeneous anisotropic shell. Our approach is based on satisfying this law within each elementary cell of the numerical grid. The main strength of the proposed algorithm is in the widely used finite difference method (FDM). It was found that the FDM accumulates numerical errors caused by numerical ´diffusion´. This artificial diffusion is a sequence of the finite difference representation of the differential operators of the original Laplace equation in a nonhomogeneous case.