Geodesic
One-dimensional finite difference schemes for splitting method realization in axisymmetric equations of the dynamics of elastic medium
Numerical methods and programming, Tome 22 (2021) no. 1, pp. 47-66.

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We construct efficient finite difference shock-capturing schemes for the solution of direct seismic problems in axisymmetric formulation. When parallelizing the algorithms implementing the schemes on multiprocessor computing systems, the two-cyclic splitting method with respect to the spatial variables is used. One-dimensional systems of equations are solved at the stages of splitting on the basis of explicit gridcharacteristic schemes and an implicit finite difference scheme of the “predictor-corrector” type with controllable artificial energy dissipation. The verification of algorithms and programs is fulfilled on the exact solutions of one-dimensional problems describing traveling monochromatic waves. The comparison of the results showed the advantages of the scheme with controllable energy dissipation in terms of the accuracy of computing smooth solutions and the advisability of application of explicit monotone schemes when calculating discontinuities.
Keywords: elastic medium; direct seismic problem; cylindrical waves; finite difference scheme; splitting method; monotonicity; dissipativity; parallel computing. 
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     author = {V. M. Sadovskii and O. V. Sadovskaya and E. A. Efimov},
     title = {One-dimensional finite difference schemes for splitting method realization in axisymmetric equations of the dynamics of elastic medium},
     journal = {Numerical methods and programming},
     pages = {47--66},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2021_22_1_a5/}
}
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V. M. Sadovskii; O. V. Sadovskaya; E. A. Efimov. One-dimensional finite difference schemes for splitting method realization in axisymmetric equations of the dynamics of elastic medium. Numerical methods and programming, Tome 22 (2021) no. 1, pp. 47-66. http://geodesic.mathdoc.fr/item/VMP_2021_22_1_a5/