Numerical Astrophysics Using Supercomputers and Adaptive Scheme

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We are able to use several kinds of supercomputers in the field of astrophysics. They are vector-parallel machines, massive parallel machines, and special purpose machines. To bring their full play, we have to choose the most effective numerical method. Although the field of numerical astrophysics is wide : from the solar system to the universe, there must be a common bottleneck which should be broken to make a breakthrough. This project were planned to answer the above point.1.The (magneto-) hydrodynamics equation is one of the most important ones in the astrophysics. Equations for the unsteady hydrodynamics are hyperbolic-type. In this case, it is shown that data are easily divided and allocated onto a number of processors. We are able to parallelize the code and achive high performance.2.On the other hand, the elliptical-type equation, such as the Poisson equation, which is also one of the most important ones in the astrophysics, is poorly parallelized. This is mainly due to the fact that it is difficult to parallelize the preconditioning of the coefficient matrix.3.As a Poisson solver, we have found that "multigrid iteration method" is fast compared to the ordinary solvers which were poorly parallelized. We have measured the CPU time necessary to solve the Poisson equation once by this method. It is only a half of the time required to solve the magnetohydrodynamics equations for one time step.4.It is shown that the nested grid technique is very efficient for a problem with a large spatial dynamic range. It uses a number of grids ; coarser grids covers a whole numerical box, while finer ones cover a region which require a fine spatial resolution.5.To proceed from the nested grid scheme to a fully adaptive one, we have to develop a method of creation/destruction of the grids. This requires the code to understand which part should be calculated closely.