Geodesic
A method for calculating invariant subspaces of symmetric hyperbolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 1019-1031
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An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations. 
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     title = {A~method for calculating invariant subspaces of symmetric hyperbolic equations},
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S. K. Godunov; V. T. Zhukov; O. B. Feodoritova. A method for calculating invariant subspaces of symmetric hyperbolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 1019-1031. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a5/

[1] Demkowicz L., Monk P., Schwab Ch., Vardapetyan L., “Maxwell eigenvalues and discrete compactness in two dimension”, Comput. Math. Appl., 40:4–5 (2000), 589–605 | DOI | MR | Zbl

[2] Hesthaven J. S., Warburton T., “High-order nodal discontionuous Galerkin methods for the Maxwell eigenvalue problem”, Philos. Trans. Roy. Soc. (London). Ser. A, 362:1816 (2004), 493–524 | DOI | MR | Zbl

[3] Godunov C. K., Uravneniya matematicheskoi fiziki, Nauka, M., 1979 | MR | Zbl

[4] Timoshenko S. P., Guder Dzh., Teoriya uprugosti, Nauka, M., 1979

[5] Van der Vegt J. J. W., van der Ven H., Boelens O. J., “Discontinuous Galerkin methods for hyperbolic partial differential equations”, Godunov methods: Theory and applications, Kluwer Acad., New York; Plenum Publs, 2001, 985–1007 | MR

[6] S. K. Godunov (red.), Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl

[7] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001 | MR

[8] Godunov S. K., Sadkane M., Robbe M., “Smoothing techniques and computation of invariant subspaces of elliptic operators”, Appl. Numer. Math., 33:1 (2000), 341–347 | DOI | MR | Zbl

[9] Godunov C. K., Sovremennye aspekty lineinoi algebry, Nauchn. kniga, Novosibirsk, 1997

[10] Godunov S. K., Zhukov V. T., Feodoritova O. B., Algoritm spektralnogo analiza dlya simmetricheskikh giperbolicheskikh uravnenii, Preprint No 91, IPMatem. RAN, M., 2005

[11] Godunov S. K., Selivanova S. V., “Eksperimenty po ispolzovaniyu rezonansa dlya spektralnogo analiza konechnomernykh kososimmetricheskikh operatorov”, Sibirskii zh. vychisl. matem., 9:2 (2006), 123–136 | MR | Zbl