Several tsunami events occurred during the past decade, and the models used for their simulation have been constantly improved. We present different numerical tools likely to improve the simulation of tsunamis, in order to obtain a fast and accurate tsunami forecast in a short amount of time. Based on a high-order discontinuous Galerkin discretization, hp-refinement is introduced, as well as parallel dynamic load balancing. Adjoint-based data assimilation is used to reconstruct the initial condition automatically from buoy measurements. The use of those numerical tools is illustrated with the simulation of the March 2011 Japanese tsunami. For this example, the model is able to reconstruct the tsunami source and accurately forecast its far-field propagation in a computational time 20 times faster than the physical propagation time. Included in a more realistic model, the presented numerical tools are most likely to improve real-time tsunami forecasts.