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The numerical modeling of the supernovae explosion mechanism poses a number of computational difficulties: One is the widely disparate timescales inherent to the problem. Another is the need for high resolution in the spatial and spectral domains in order to fully resolve the features present in the problem. And a third difficulty lies in the need for high accuracy in the simulation because of the marginality of the explosion mechanism. In order to address and overcome these difficulties we have formulated a fully implicit general relativistic adaptive mesh method for numerically simulating the explosion mechanism of core collapse supernovae. We discuss the method and its performance characteristics along with the results of our simulations in this paper.
