Geodesic
Development of an efficient parallel Poisson equation solver for the simulation of protoplanetary disk evolution
Numerical methods and programming, Tome 10 (2009) no. 1, pp. 116-122.

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A Poisson equation solver is proposed. The main idea of the solver is taking the features of the problem under study into account. Since the problem is nonstationary, it is possible to solve the Poison equation quickly by means of simple iteration methods. The consideration of the axial symmetry of the disk allows one to construct a domain decomposition with a very small amount of interprocessor communications. In addition, the infinitely thin disk approximation allows one to speed up the computations when using the iteration methods. The paper was prepared on the basis of the authors' report at the International Conference on Parallel Computing Technologies (PaVT-2009; http://agora.guru.ru/pavt2009).
Keywords: Poisson equation; nonstationary problems; iteration methods; protoplanetary disk. 
@article{VMP_2009_10_1_a13,
     author = {V. A. Vshivkov and A. V. Snytnikov},
     title = {Development of an efficient parallel {Poisson} equation solver for the simulation of protoplanetary disk evolution},
     journal = {Numerical methods and programming},
     pages = {116--122},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a13/}
}
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V. A. Vshivkov; A. V. Snytnikov. Development of an efficient parallel Poisson equation solver for the simulation of protoplanetary disk evolution. Numerical methods and programming, Tome 10 (2009) no. 1, pp. 116-122. http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a13/