Three dimensional numerical relativity using parallel super computers

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I have developed numerical simulation codes for studying coalescing neutron star binaries and radiation of gravitational waves, and obtained a stabie code which follows the evolution of coalescing neutron star binaries with a high precision. The basic structure of the code includes :As for the coordinate condition, the pseudo-minimal distortion condition for the spatial coordinate and the maximal slicing condition for the time coordinate are used. At first, I adopted the conformal slicing for the time coordinate but was confronted with unstable modes in the evolution of the lapse function. Then I used the maximal slicing instead.Six elliptic partial differential equations mush be solved for the laps function, shift vector and conformal factor at each time step. They are solved using a preconditioned conjugate gradient method that can be fully vectorizable and parallelizable, but in order to achieve a high speed calculation the program must be tuned to high degree for some kind of super computer.The general relativistic hydrodynamics equations are solved using van Leer's scheme with TVD and the evolution equations for the metric tensor are solved using the CIP method.Gravitational waves can be obtained simply from the metric perturbation with the conformal slicing, but gauge-invariant gravitational wave extraction is needed with the maximal slicing. Although it has not yet implemented, I found that a simple metric perturbation gives a good estimate for the gravitational waves in comparison the results with both slicing conditions.To obtain the final results in coalescing neutron star binaries and the gravitational radiation, more computer power is necessary, but the code has scalableness and coalescing neutrons star binaries will be studied soon using the code on new super computer at National Astronomical Observatory Japan and/or the High Energy Accelerator Research Organization.