Two New Approaches in Solving the Nonlinear Shallow Water Equations for

One key component of tsunami research is numerical simulation of tsunamis, which helps us to better understand the fundamental physics and phenomena and leads to better mitigation decisions. However, writing the simulation program itself im-poses a large burden on the user. In this survey, we review some of the basic ideas behind the numerical simulation of tsunamis, and introduce two new approaches to construct the simulation using powerful, general-purpose software kits, PETSc and FEPG. PETSc and FEPG support various discretization methods such as finite-difference, finite-element and finite-volume, and provide a stable solution to the numerical problem. Our application uses the nonlinear shallow-water equations in Cartesian coordinates as the governing equations of tsunami wave propagation. Key words