To understand the physical phenomena and to be able to propose countermeasures/improvements, simulation tools to perform computations of the entire dynamical system including subground, track structure and the train have been developed. In particular, effort has been devoted to the special wave propagation problem related to high-speed trains running at soft ground materials. As the speed of the train approaches and exceeds the natural (Rayleigh) wave propagation velocity of the ground material, shock waves similar to a sonic boom originate from the onrushing train. The problem area contains several computational challenges since it implies efficient techniques to handle time integration of large-scale problems, infinite domains, non-linear material response etc.

Efficient solvers based on a combination of multigrid, error estimations and adaptive refinement have been developed to reach acceptable execution times. The solution time is substantially reduced compared to conventional implicit solvers based on factorization. Moreover, an indefinite system from the Lagrange multiplier approach to handle constraint equations requires additional preconditioning to guarantee convergence and reduce the number of iterations.

In the paper a number of numerical examples from railway applications are presented. Results from computation where the train is represented as a collection of moving loads as well as a multi body system with complete train-track interaction are demonstrated.