A METHOD FOR FINE-GRAIN PARALLELIZATION OF 2D AND 3D TRANSPORT PROBLEMS ON NON-ORTHOGONAL GRIDS

A.V. Alekseev, A.A. Nuzhdin, R.M. Shagaliev
VANT. Ser.: Mat. Mod. Fiz. Proc 2001. Вып.2. С. 3-10.

A method is proposed for fine-grain parallelization of numerical solution of 2D transport equation, intended for using multiprocessor with distributed memory allowing computations on a number of computers up to 100 and more.
   The method is based on the principle of the geometry decomposition of the original system to subdomains (paradomains). The division into paradomains is performed regularly by rows and columns so that data amount to be equal. In general case such a division results in a process topology in the form of 2D grid (by rows and columns). As this takes place, each processor stores data for a special paradomain but not for the whole problem.
   Each paradomain for a current direction is solved with internal boundary conditions computed at a current iteration, which allows holding solution accuracy and preventing total iteration amount increase as compared with a sequential technique.
   The idle time of processors is minimized through their loading with useful additional computational work, that is computation of intermediate coefficients. Later grid values of a particle flow function are expressed through these coefficients.
   For interprocessor messaging the library for MPI parallel coding interface (Message Passing Interface) is used.
   The results of numerical studies of parallelization efficiency for the method developed are presented.
   Some extension of this method to the parallelizing 3D transport problems is given.