Numerical earthquake models often use Green's functions for which the compute time increases with N^2, where N is the number of elements defining the fault(s) used in the model. For realistic models of earthquakes it is necessary to use small elements and thus very large N. Especially for models that require considerable computation in each time step, such as the rate and state friction laws, the limitations of computer time severely restricts the size of the models that can be studied. The Fast Multipole Method involves grouping elements together that are removed from the location of interest and the compute time increases with N log N. Testing of this method on an earthquake problem suggests that it may offer much promise for more realistic modeling of earthquakes.
