Tsunamis like those in Indonesia in 2004 and Japan in 2011 have shown like never before the destructive power of this natural disaster. This highlighted the importance of fast and accurate simulations for forecasting. We present a fully GPU-accelerated tsunami model for large domains that delivers results within minutes with high accuracy and efficient resource use. By using just three GPUs, results for the Indian Ocean were obtained in 15 min. This allows for fast evacuation and risk decisions.