### Tsunami Modeling

Natural catastrophic disasters like tsunamis commonly strike with little warning. For most people, tsunamis are underrated as major hazards. People sometimes wrongly believe that they occur infrequently and only along distant coasts. Tsunamis are usually caused by earthquakes. Seismic signals can give some margin of warning since the speed of tsunami waves travels at 1/30 the speed of seismic waves. Still there is little time between the creation of the tsunami and its impact - typically between one to two hours for distant earthquakes and much less for locations in the near field region. Having fast response mechanisms at the onset of tsunami waves saves lives. Codes that can deliver output in the course of a few minutes are critical to providing sufficient warning to coastal regions.

Radial basis functions (e.g. [1]) are a novel method to solve partial differential equations. They represent a gridless approach [2] and require fewer grid points for solving the partial differential equations because of their high accuracy. The authors illustrate their use in the shallow-water equations together with their implementation on a GPU with Jacket software. The authors have provided results on the comparison in computational times of CPU versus GPU for both linear shallow-water equations and a swirling flow problem in atmospheric flows.

The faster growth curves in the speed of GPUs relative to CPUs have spawned a new area of development in computational technology. GPUs offer much potential for solving evolutionary partial differential equations and producing attendant visualizations. The authors were concerned with modeling tsunami waves where computational time is of extreme essence in broadcasting warnings. They employed Jacket software and an NVIDIA board on a MacBook Pro to test the efficacy of the GPU on the set of shallow-water equations and compared the relative speeds between CPU and GPU for two types of spatial discretization based on second-order finite differences and radial basis functions. Results showed the GPU implementations produced measurable speed increases for the finite-difference method and the RBF scheme. The Jacket and GPU solution also improved speed with an atmospheric dynamics problem of swirling flows (solid body rotation) over a spherical surface. The time steps employed for the RBF method are larger than those used in finite-differences because of fewer nodal points are needed by RBF. Thus, RBF acting in concert with GPU holds great promise for tsunami modeling because of the spectacular reduction in the computational time.

**RBF Implementation**

Jacket software by AccelerEyes eliminates the need to and hassle of compiling individual CUDA kernels into MEX files for use in MATLAB. Jacket was used to run an RBF simulation on the GPU with a time to solution not available by other alternatives. Using Jacket, the authors were able to access the GPU without leaving the MATLAB environment. Jacket is a software platform that masks the complexity of programming a GPU, eliminating the need for the user to know any GPU-specific programming languages or architectures. Instead of writing CUDA kernels, one just needs to use GPU datatypes in the MATLAB environment indicating matrices which might benefit from data parallel execution. The following is an example of how to implement MATLAB code on the GPU using Jacket.

- A = eye(5); % creates a 5x5 identity matrix
- A = gsingle (A); % casts A from the CPU to the GPU
- A = A * 5; % multiplies A by a scalar on the GPU
- A = double (A); % casts A from the GPU back to the CPU

The radial basis function simulation was executed on an NVIDIA 8600 GPU using Jacket. Comparing the simulation that ran strictly on the CPU of a MacBook Pro to the simulation that implemented a GPU, the following speed improvements were recognized:

This simulation contained four hundred time steps and a grid size of 30 by 30. Overall, running a RBF simulation in conjunction with the GPU produces the fastest results, allowing the shortest time in issuing a tsunami warning.

**Authors:**

- DAVID A. YUEN, Minnesota Supercomputing Institute, University of Minnesota, Minnesota
- JESSICA SCHMIDT, Saint Scholastica College, Duluth, Minnesota
- ERIK O.D. SEVRE, Minnesota Supercomputing Institute, University of Minnesota, Minnesota
- NAN ZHANG, Medical School, University of Minnesota Minnesota
- GRADY B. WRIGHT Dept. of Mathematics , Boise State University, Boise, Idaho
- Cecile Piret, National Center for Atmospheric Research, Boulder, Colorado
- Yingchun Liu, Minnesota Supercomputing Institute, University of Minnesota
- Natasha Flyer, National Center for Atmospheric Research, Boulder, Colorado

- [1]. Fornberg, B. and Piret, C., A stable algorithm for at radial basis functions on a sphere, SIAM J. Sci. Comput. 200, 178-192, 2007.
- [2]. Fasshauer, G.E., Meshfree Approximation Methods with Matlab, World Scientific Publishing, Singapore, 2007.

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