HR: 0800h
AN: S11A-0997    [Abstracts]
TI: A 3D Mimetic Finite Difference Method for Rupture Dynamics
AU: * Ely, G
EM: gely@ucsd.edu
AF: University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093 United States
AU: Minster, J
EM: jbminster@ucsd.edu
AF: University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093 United States
AU: Day, S
EM: day@moho.sdsu.edu
AF: San Diego State University, 5500 Campanile Drive, San Diego, CA 92182 United States
AB: We are developing a method for solving earthquake rupture dynamics problems on structured curvilinear meshes. The advantage of a curvilinear mesh over a rectangular mesh is that it can accommodate free-surface topography as well as non-planar fault geometry. The advantages of using a structured mesh over an unstructured mesh (as used in many finite element methods) is simplicity and computational efficiency. Structured meshes also make a number of computational tasks easier, such as parallelization, or coupling with other codes that use similar structured meshes. To build the discretized equations of motion on a structured, yet non Cartesian mesh, we use a mimetic method, so named because it takes special care to mimic the important conservation properties of the original equations of motion. We begin by writing the equations of motion in terms of gradient and divergence operators. We then derive a discrete grad (or div) operator by differentiating an interpolation function of the discrete variable. Next, that grad (or div) operator is plugged into a discrete analog of Gauss' Identity and manipulated to find the adjoint div (or grad) operator. We use a computer algebra system to handle the manipulations, which is practically essential for the 3D case because of the extreme lengths of the expressions to be coded. The code is currently implemented as a "rapid prototype" in MATLAB and undergoing validation prior to conversion to a high performance language. We compare results for simple types of rupture that have analytical solutions.
DE: 7209 Earthquake dynamics and mechanics
SC: Seismology [S]
MN: 2004 AGU Fall Meeting