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David Alexander Yuen

Research Report

During my month long stay at ERI between October 12 and November 12, 2008, I have developed some ties which will pave for my coming here in the near future. They are:

(1) Starting a brand-new project with H. Shimizu of ERI in the application of electrical conductivity in causing localized melting at the core-mantle boundary by Ohmic dissipation due to electrical quake-like phenomena (den-shin) developed at local areas under the core-mantle boundary found in very high-resolution geodynamo simulations. Also involved in this venture are A. Sakuraba of Todai, N. Takeuchi of ERI and Ono from JAMSTEC. We expect a new area of multi-disciplinary area of research will be created soon, as this project involves seismology, mineral physics, computational technology and electrical conductivity.

(2) During this visit at the Earthquake Research Institute in Tokyo, Cecile Piret from NCAR in Boulder, Colorado who accompanied me worked in tsunamis on the linear long wave system of equations with and without dispersion with Saito-san. She used the Radial Basis Functions (RBF) method combined with the Runge Kutta ODE solver of the 4th order to solve these equations on a 2D doubly periodic domain. The solutions obtained via RBFs and via a commonly used finite difference solver such as the staggered leapfrog (SL) method were compared. We notice that non only does the RBF method require less data points than the SL method, but also that the time steps required by RBFs are significantly larger than the ones needed by the SL method. In addition to this, the RBF method does not require the data to be on a grid. She and Saito can therefore refine the nodes on certain areas, such as the ones close to the coastline, which are important to represent accurately when solving these types of equations. Although a lot of progress has still to be made, we see that the RBF method has lots of potential for solving the equations that model the tsunami phenomena.

In addition to the above accomplished tasks, I wrote a short paper on the application of graphical processing unit (GPU) and radial basis functions to tsunami wave propagation. I also gave three talks on various topics, ranging from tsunamis to seismic imaging using curvelets. Cecile Piret gave also one talk on using RBFs on modelling tsunami wave propagation.