4.8 The Binary Black Hole 4 Cauchy-Characteristic Matching4.6 Cauchy-Characteristic Matching for 3D

4.7 3D Cauchy-Characteristic Matching 

The most important application of CCM is anticipated to be the binary black hole problem. The 3D Cauchy codes now being developed to solve this problem employ a single Cartesian coordinate patch [141]. A thoroughly tested and robust 3D characteristic code is now in place [30Jump To The Next Citation Point In The Article], ready to match to the boundaries of this Cauchy patch. Development of a stable implementation of CCM represents the major step necessary to provide a global code for the binary problem.

From a cursory view, the application of CCM to this problem might seem routine, tantamount to translating into finite difference form the textbook construction of an atlas consisting of overlapping coordinate patches. In practice, it is an enormous project.

A CCM module has been constructed and interfaced with Cauchy and characteristic evolution modules. It provides a model of how Cauchy and characteristic codes can be pieced together as modules to form a single global code. The documentation of the underlying geometrical algorithm is given in Ref. [28]. The main submodules of the CCM module are:

The CCM module has been calibrated to give a second order accurate interface between Cauchy and characteristic evolution modules. When its long term stability has been established, it will provide an accurate outer boundary condition for an interior Cauchy evolution by joining it to an exterior characteristic evolution which extracts the waveform at infinity.



4.8 The Binary Black Hole 4 Cauchy-Characteristic Matching4.6 Cauchy-Characteristic Matching for 3D

image Characteristic Evolution and Matching
Jeffrey Winicour
http://www.livingreviews.org/lrr-2001-3
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