A data parallel pseudo-spectral semi-implicit magnetohydrodynamics code

The set of eight nonlinear partial differential equations of magnetohydrodynamics (MHD) is used for time dependent simulations of three-dimensional (3D) fluid flow in a magnetic field. A data parallel code is presented, which integrates the MHD equations in cylindrical geometry, combining a semi-implicit time integration with a pseudo-spectral treatment of the poloidal and longitudinal directions. The semi-implicit method is devised to lift the severe CFL-condition imposed by the fastest waves. In the radial direction, we use centered finite differences on a staggered mesh. Together with the semi-implicit method, this leads to tridiagonal systems to be solved for each 2D Fourier mode. The parallelism is required to fully resolve small-scale dynamics in MHD simulations at affordable CPU costs. It is obtained by performing the 2D FFTs in an embarrassingly parallel way, and by solving the tridiagonal systems using a pipelined elimination algorithm. We discuss the scalability of the full code for a CM-Fortran implementation.