Geodesic
Tiling optimization for the solution of two-dimensional time-dependent heat equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 631-641

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Tiling optimization for the solution of the Dirichlet problem for the two-dimensional heat equation on computers with distributed memory is investigated. Estimates of the amount of communications and computations are obtained. The tiling optimization problem is reduced to the minimization of a function that explicitly expresses the dependence of the execution time on the tile size and the parameters of the target supercomputer – the dimension and size of the computing environment, processor performance, initialization time, and capacity of the communication channels. 
@article{ZVMMF_2011_51_4_a6,
     author = {S. V. Bakhanovich and P. I. Sobolevskii},
     title = {Tiling optimization for the solution of two-dimensional time-dependent heat equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {631--641},
     publisher = {mathdoc},
     volume = {51},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a6/}
}
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S. V. Bakhanovich; P. I. Sobolevskii. Tiling optimization for the solution of two-dimensional time-dependent heat equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 631-641. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a6/