Numerical studies of convection and magnetohydrodynamic (MHD) dynamo action in a rotating spherical shell of compressible fluid are carried out, motivated by the problem of magnetic field generation in the geodynamo. These calculations are made in a Cartesian framework using a high-order finite-difference code: the Pencil-code. The Pencil-Code uses an expUcit sixth-order centred finite-difference scheme in space, and an explicit thirc order Runge-Kutta scheme in time, and operates on 'pencils' (array sections) in one dimension in a cache-efficient way. A parallel decomposition of the spatial domain is aade in the two orthogonal dimensions, with the communication of boundary elements being handled by Message Passing Interface (MPl).