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Because of improvements in offshore tsunami observation technology, dispersion phenomena during tsunami propagation have often been observed in recent tsunamis, for example the 2004 Indian Ocean and 2011 Tohoku tsunamis. The dispersive propagation of tsunamis can be simulated by use of the Boussinesq model, but the model demands many computational resources. However, rapid progress has been made in parallel computing technology. In this study, we investigated a parallelized approach for dispersive tsunami wave modeling. Our new parallel software solves the nonlinear Boussinesq dispersive equations in spherical coordinates. A variable nested algorithm was used to increase spatial resolution in the target region. The software can also be used to predict tsunami inundation on land. We used the dispersive tsunami model to simulate the 2011 Tohoku earthquake on the Supercomputer K. Good agreement was apparent between the dispersive wave model results and the tsunami waveforms observed offshore. The finest bathymetric grid interval was 2/9 arcsec (approx. 5 m) along longitude and latitude lines. Use of this grid simulated tsunami soliton fission near the Sendai coast. Incorporating the three-dimensional shape of buildings and structures led to improved modeling of tsunami inundation. [ABSTRACT FROM AUTHOR]