Geodesic
Efficient algorithm for proper-time computations of long electromagnetic phenomena in a bounded computational domain
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 10, pp. 1826-1836 Cet article a éte moissonné depuis la source Math-Net.Ru

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Nonreflecting artificial boundary conditions (ABCs) and an efficient algorithm for their implementation are constructed, which replace difference Maxwell equations in a vacuum solved in proper time in a region surrounding the computational domain. One time step of the algorithm requires $O(T_f^1h^{-4})$ time rather than $O(T_f^4h^{-4})$ time taken in the direct computation without using ABCs. This makes it possible to compute certain electrodynamic problems at long times. 
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S. V. Petropavlovsky. Efficient algorithm for proper-time computations of long electromagnetic phenomena in a bounded computational domain. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 10, pp. 1826-1836. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_10_a7/

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