The dynamic behaviour of a railway system is in¯uenced by the interaction of its three subsystems: the vehicles, the rail construction itself and the subsoil. In this paper, the subsoil is considered as a linear-elastic layered half-space. Integral transformations are used for the analysis of this system: Fourier transformation for the time/frequency domain and for the space/wavenumber domains with respect to the horizontal coordinates. One arrives at an ordinary differential equation for the vertical direction, by which different layers or continuously changing elastic properties can be taken into account in an ef®cient manner. The ef®-ciency of the transformation technique depends substantially on the effort necessary for the inverse transformation. A substantial reduction of data can be achieved in an error-controlled procedure if a wavelet transformation is applied as an additional transformation. The calculations are illustrated by solutions of several examples of moving time-dependent loads, particularly of a train model with four vehicles idealized by moving forces, time depending as if they were passing a rigid surface with a given roughness.

The article presents a fast numerical algorithm for calculating the response of a halfspace under any surface loads. Under certain conditions there exists an analytical solution to the problem in the Fourier domain. To get the desired response, a numerical inverse Fourier transform of this analytic solution has to be made. By using a wavelet decomposition, the proposed algorithm can reduce the calculation time signi®cantly, thus allowing the computation of complex problems. As an example, the response of the beam-halfspace coupled system under moving load is presented.

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In this work, we present recent enhancements and new functionalities of our flow solver in the partial differential equation framework Peano. We start with an introduction including an overview of the Peano development and a short description of the basic concepts of Peano and the flow solver in Peano concerning the underlying structured but adaptive Cartesian grids, the data structure and data access optimisation, and spatial and time discretisation of the flow solver. The new features cover geometry interfaces and additional application functionalities. The two geometry interfaces, a triangulation-based description supported by the tool preCI-CE and a built-in geometry using geometry primitives such as cubes, spheres, or tetrahedra allow for the efficient treatment of complex and changing geometries, an essential ingredient for most application scenarios. The new application functionality concerns a coupled heat-flow problem and two-phase flows. We present numerical examples, performance and validation results for these new functionalities.

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