The purpose of this project is to integrate a three- dimensional model of the geodynamo by using a novel numerical method. In common with most current research, the Earth's fluid core will be represented by a convecting Boussinesq fluid. Traditional numerical methods cannot, by many orders of magnitude, simulate the effects of the large rotational (Coriolis) force that so potently affects the convective regime of the core; the new method promises to represent them within an order of magnitude. The new procedure, which depends on an unusual choice of computational grid, has been tested on so- called "intermediate models" of the geodynamo, which are axisymmetric over-idealizations of the magnetohydrodynamics (MHD) of the core, and has been found to perform well. The next logical step is to include geophysically realistic (i.e. dynamically determined) asymmetries. The new integrations will hopefully help settle one of the central issues of geodynamo theory of this decade: whether or not the MHD of the core is controlled at the core-mantle boundary.