Algorithms and software for linear and nonlinear MHD simulations

The very different spatial and temporal scales inherent in the dissipative MHD model impose severe requirements on the numerical simulations, which have to be met by appropriate methods. The numerical approximation discussed is based on the finite-element method, where space-time discretization and semi-discretization are included. Specific advanced methods, such as adaptive mesh, multigrid, normal-mode analysis and semi-implicit schemes are presented. Important features of present and future supercomputers are being addressed.