Geodesic
Parallel computations for the simulation of seismic waves on the basis of the additive Schwartz method
Numerical methods and programming, Tome 13 (2012) no. 4, pp. 525-535 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Laguerre time transform for the elastic wave equations leads to a definite spatial operator independent of a separation parameter. This allows one to perform parallel computations on the basis of Schwartz alternations using a domain decomposition with overlapping. On each alternation step, the resulting system of linear algebraic equations in each subdomain is solved independently, so one can use a direct solver on the basis of the LU-decomposition. Since the spatial operator is independent of separation parameters, this decomposition can be performed only once and be saved in RAM for each elementary subdomain to use for all right-hand sides. This approach is implemented and the corresponding software for high performance computers with hybrid parallel architecture is developed. A number of numerical results illustrating the analysis of scalability are discussed.
Keywords: Laguerre transform; definite operator; additive Schwartz method; parallel computations; scalability. 
@article{VMP_2012_13_4_a5,
     author = {M. A. Belonosov and K. Kostov and G. V. Reshetova and V. A. Tcheverda},
     title = {Parallel computations for the simulation of seismic waves on the basis of the additive {Schwartz} method},
     journal = {Numerical methods and programming},
     pages = {525--535},
     year = {2012},
     volume = {13},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2012_13_4_a5/}
}
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M. A. Belonosov; K. Kostov; G. V. Reshetova; V. A. Tcheverda. Parallel computations for the simulation of seismic waves on the basis of the additive Schwartz method. Numerical methods and programming, Tome 13 (2012) no. 4, pp. 525-535. http://geodesic.mathdoc.fr/item/VMP_2012_13_4_a5/