# Hardware Acceleration of Tsunami Wave Propagation Modeling in the Southern Part of Japan
## 1 Introduction  
To address the problem of timely reporting of the danger of a tsunami wave at a particular coastal zone location, we apply the facilities of modern computer architectures to accelerate the numerical simulation of tsunami wave propagation. The main goal of this paper is to demonstrate the advantages of a new super rapid method for modeling tsunami wave propagation. We do not wish to obtain the detailed wave height maxima distribution along the specified coast. According to [1], rather strong earthquakes (and, therefore, dangerous tsunami waves) happen with an approximately 150-year period in the part of the Nankai subduction zone near Shikoku Island and Kii Peninsula. As the last high-impact event in the region was in 1854 (166 years ago), the next one can be expected in the near future. We are therefore running numerical experiments via digital bathymetry which approximates the real bottom topography of a corresponding water area. Our aim is to use just a regular modern personal computer (PC) and to achieve valuable performance gain exploiting graphic processing units (GPUs) and field-programmable gate arrays (FPGAs) as co-processors. We propose a specific hardware configuration and the corresponding modeling code. The following general scheme for tsunami danger prediction is assumed. The measurements of the propagating tsunami wave (time series) are obtained in real-time mode from DART (Deep-ocean Assessment and Reporting of Tsunami) buoys ([[https://nctr.pmel.noaa.gov/Dart/](https://nctr.pmel.noaa.gov/Dart/)]([https://nctr.pmel.noaa.gov/Dart/](https://nctr.pmel.noaa.gov/Dart/))) or any other real-timepressure sensor system, like the DONET (Dense Ocean floor Network system for Earthquakes and Tsunamis) pressure gauge network [2]. Based on the measurement data, the initial seabed displacement should be determined. In practice, we reconstruct the initial sea surface displacement. There are several ways to do it; see [3; 4]. Here, we refer to a fast method using an orthogonal decomposition algorithm; see [5]. Then, finally, tsunami wave propagation over the water area under consideration is numerically calculated. We study only this part (the calculation of tsunami wave propagation) to reduce the time required for the numerical study. Among the most popular software instruments, the MOST (Method of Splitting Tsunamis) software package should be highlighted. This official instrument of the U.S. National Oceanic and Atmospheric Administration (NOAA) tsunami warning centers simulates all tsunami phases--generation, propagation, and the inundation of dry land [6; 7]. The calculation of wave propagation over the chosen water area is based on numerical solution of linear or nonlinear shallow water differential equations. We compare the precision and execution time of our software with the realization of the MOST algorithm for computing tsunami propagation from the source to a shoreline. It follows the theory of difference schemes for partial differential equation (PDE) systems, according to which, for stable calculation, the wave advancement during the time step is required to be less than the spatial step of the computational grid. This means that calculation of the wave propagation in big enough areas with a fine grid may require too much time, even on a modern PC. The nested grids approach can help in this case. The second way suggests using the advantages of modern computer architectures. In particular, it includes GPUs and FPGAs. It is common knowledge that a tsunami warning system (even if we address only its modelling part) should include three basic stages, namely, generation, wave propagation, and the inundation of dry land. In this paper we consider only the wave propagation part in order to make the computations faster but keep sufficient accuracy. So, we suppose that the tsunami wave is due to a certain disturbance of the sea surface. This initial disturbance serves as the initial conditions in the governing evolution-type equations. We also do not touch upon the inundation mapping questions.