This paper presents a dynamic domain decomposition (D³) technique for implementing the parallelization of the piecewise parabolic method (PPM) for solving the ideal magnetohydrodynamics (MHD) equations. The key point of D³ is distributing the work dynamically among processes during the execution of the PPM algorithm. This parallel code utilizes D³ with a message passing interface (MPI) in order to permit efficient implementation on clusters of distributed memory machines and may also simultaneously exploit threading for multiprocessing shared address space architectures. 3D global MHD simulation results for the Earth’s magnetosphere on the massively parallel supercomputers Deepcomp 1800 and 6800 demonstrate the scalability and efficiency of our parallelization strategy.