??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(?????????????????????????????u(???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(??????????????????????????????u???????????????????ÔÚ??????????u(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(???????????????????˜˜??????????u(???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u?????????? ???????????????????u(???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(????????????????????????????u(n???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(???????????????????êê??????????u(?????????????????????????????u(n???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????$???????????????????u(????????????????????????????u(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(??????????????????????????????u(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(????????????????????????????u(n???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(???????????????????ee??????????u(??????????????????]]??????????????????????????????????????????????????????????????????????????????????????????1) ????????????????????????????????????????????u(n???????????????????????????u(??????????????????GG????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????u(n???????????????????2) ????????u(???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????ical (General) Relativity Overview This field solves numerically the deceptively innocent equation proposed by Einstein in 19XX1????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????excepgions oxtreme gravitatial fields. This general theory has been tested in a few well-known cases (such as the be????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????llectual curiosity (surely we must try to solve the fundamental macroscopic equations of science) and phenomenological value to ???????????????????????????????????????3) ?????????????????????????????????????????????????????????????????????????????????????????????????????????+?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????from which no information can escape. Einstein's equations can be analy4) tically solved for single black holes in equilibrium but ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????y special features, which both distinguish this field and put it outside most of the forefront research in the algorithm and app???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? complicated nonlinear version of Maxwell's equations. Correspondingly electromageful test environment for???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? treat space and time symmetrically and have a rather different structure from those coming from other fields simulating physica????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????stinguish "science", "numerical problems" and "coordinate system artifacts" There are many formulations of Einstein equations, d????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????ere the strong fields probably require a different coordinate choices. Most distinctive is the interior boundary condition, whic????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????merically stable boundary conditions is not trivial. Physics implies no information specified inside the black hole can propagat???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? results have been obtained in a regime where no condition at the inner boundary (simply excision) is required. The problem bec????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)???n????)?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????to extract the gravitational wave structure as the black holes rotate around each other and eventually spiral into cosmic union.???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? without dissipation all contribute to the numerical challenge. Current Situation As with computational electromagnetics, one c????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????e results. A large Grand Challenge "Binary Black Hole (BBH)" project recently finished and although much important progress was ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????project did use several parallel computing technologies described in other sections of the book. In fact the DAGH distributed da???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? Perl also proved to be to rigid to allow fast development on the Fortran side; changes such as introducing another field variab????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????n the proposal was initially written but adaptive meshes were not used in production during the five-year Grand Challenge projec????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????ingenious physics insight to the inner boundary conditions is all that is needed. Alternatively or more likely in addition, this????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????ely seen as transparent bubbles. They will become clearer on following figures.  Fig 2: The Black Holes showing clearly that th????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????Computational Science" Acto Acta Numerica (1999) pp. 1-44. Numerical relativity: challenges for computational science, Gregory B????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????tsdam.Review failure of automatic mapping to DAGH (Haupt), current status Good have nifty picture such as pants diagram of merg????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????A ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????AF`??????`?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????‰?????‡??????????????` ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????A?`H?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????