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Wave propagation in solid materials is of great interest in many engineering applications. The fact that the area of interest changes with time creates a number of computational problems such as the need for a mesh density varying in space and time. This means that the mesh must be continuously updated and controlled, rendering a large demand of computer effort. In certain applications like railway mechanics there are mobile loads. A load speed close to the natural speed in the underlying soil causes specific problems, shock waves being one of them. The transmitted waves have to leave the defined finite element domain without reflection, which imposes a need for certain modelling methods. The paper will deal with quality controlled FE-procedures for wave propagation including error estimation and mesh refinement/coarsening. As an application an important problem from railway mechanics is considered. When a high-speed train approaches an area with decreasing thickness of underlying soft soil on a stiff rock it is expected that the reflection of the wave will increase the total amplitude of the wave. We will study this problem with the procedures described above in full 3D with partly absorbing boundaries

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.