The correct prediction of the propagation of noise and vibration in soil or air is of great relevance with respect to environmental protection in Europe. Here, the numerical modelling of wave propagation in unbounded domains is required. This task belongs to the major research fields in computational mechanics, since the correct description of radiation damping in infinite media is a challenge, and the available information on material and loading data is frequently uncertain. The main objective of this proposal is to further develop a numerical method for the realistic simulation of large-scale wave propagation processes in unbounded domains. During the outgoing phase the scaled boundary finite element method developed at the outgoing host will be combined with the mixed-variables technique derived at the return host, thus the project builds on the strengths of both partners. During the return phase the applicant will substantially widen her scientific profile by extending the developed algorithms to include aspects of generalized uncertainty modelling. Carrying out the project, the fellow will acquire complementary skills such as skills in writing and reviewing scientific papers, presentation skills, teaching experience and research management skills. This will be achieved through participation in conferences, joint organization of a mini-symposium on SBFEM, co-teaching of a final year subject and joint supervision of PhD projects during the outgoing phase. After the fellowship the applicant intends to apply for funding of a junior research group under her leadership. Her long-term career objective is a professorship at a European university. By providing the prerequisites to obtain such a position, in particular through managing this multi-partner project and by providing international research experience, the project strongly contributes to the applicant's career development and the enhancement of European excellence in computational mechanics.