First I will list the most important mathematical methods and numerical algorithms used for tsunami simulations in general. Thereafter I will go more into detail about simulating tsunamis generated by earth-asteroid collisions, and in particular an impact in the paleo Barents Sea (north of Norway) 142 million years ago. Spectacular tsunamis arising from asteroid impacts may have a significant influence on the life on earth and are therefore of interest to geologists and biologists. The impact 142 million years ago has been studied in detail, and simulating the tsunami propagation requires dispersive and non-linear wave equations solved by implicit methods. Due to the finite signal speed in such models, domain decomposition methods are particularly attractive, both for flexible model formulation and parallelization. The numerical methods used so far and the results obtained will be presented. Then I will cover future wishes for grid resolution, model formulations, and numerical algorithms.