Viktor Solomonovich Ryaben'kii and his school (on his 90th birthday)

S. K. Godunov   ; V. T. Zhukov   ; M. I. Lazarev   ; I. L. Sofronov   ; V. I. Turchaninov   ; A. S. Kholodov   ; S. V. Tsynkov   ; B. N. Chetverushkin   ; Ye. Yu. Epshteyn

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 6, pp. 1183-1210

Bibliographie

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[21] A. A. Reznik, V. S. Ryaben'kii, I. L. Sofronov, V. I. Turchaninov, “An algorithm of the method of difference potentials”, U.S.S.R. Comput. Math. Math. Phys., 25:5 (1985), 144–151 | DOI | MR | Zbl

[22] I. L. Sofronov, “A numerical iterative method for solving regular elliptic problems”, U.S.S.R. Comput. Math. Math. Phys., 29:3 (1989), 193–201 | DOI | MR | Zbl

[23] V. S. Ryabenkii, I. L. Sofronov, “Chislennoe reshenie prostranstvennykh vneshnikh zadach dlya uravnenii Gelmgoltsa metodom raznostnykh potentsialov”, Chislennoe modelirovanie v aerogidrodinamike, Nauka, M., 1986, 187–201 | Zbl

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[26] V. S. Ryaben'kii, S. V. Tsynkov, “Artificial boundary conditions for the numerical solution of external viscous flow problems”, SIAM J. Numer. Anal., 32:5 (1995), 1355–1389 | DOI | MR | Zbl

[27] V. S. Ryaben'kii, V. A. Torgashov, “The method of difference potentials for the numerical solution of an interior problem on plane flow of a viscous incompressible fluid”, Russian Acad. Sci. Dokl. Math., 50:1 (1995), 108–113 | MR | Zbl

[28] V. S. Ryabenkii, V. A. Torgashov, “Bezyteratsionnyi sposob resheniya neyavnoi raznostnoi skhemy dlya uravnenii Nave–Stoksa v peremennykh: zavikhrennost i funktsiya toka”, Matem. modelirovanie, 8:10 (1996), 100–112 | MR | Zbl

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[30] M. N. Mishkov, V. S. Ryabenkii, “Issledovanie iskusstvennykh granichnykh uslovii, postroennykh s pomoschyu periodizatsii i vvedeniya malogo parametra, dlya zadach dozvukovogo obtekaniya”, Matem. modelirovanie, 10:9 (1998), 87–98 | MR | Zbl

[31] D. S. Kamenetskii, “Difference potentials and parameterization of solutions of homogeneous difference equations”, Comput. Math. Math. Phys., 38:11 (1998), 1754–1767 | MR | Zbl

[32] D. S. Kamenetskii, “Difference generalized Poincaré–Steklov operators and potentials with densities from a jump space”, Comput. Math. Math. Phys., 39:8 (1999), 1275–1282 | MR | Zbl

[33] S. V. Tsynkov, “On the definition of surface potentials for finite-difference operators”, J. Sci. Comput., 18:2 (2003), 155–189 | DOI | MR | Zbl

[34] S. V. Tsynkov, “An application of nonlocal external conditions to viscous flow computations”, J. Comput. Phys., 116:2 (1995), 212–225 | DOI | MR | Zbl

[35] S. V. Tsynkov, E. Turkel, S. Abarbanel, “External flow computations using global boundary conditions”, AIAA J., 34:4 (1996), 700–706 | DOI

[36] S. V. Tsynkov, V. N. Vatsa, “Improved treatment of external boundary conditions for three-dimensional flow computations”, AIAA J., 36:11 (1998), 1998–2004 | DOI

[37] S. V. Tsynkov, “External boundary conditions for three-dimensional problems of computational aerodynamics”, SIAM J. Sci. Comput., 21:1 (1999), 166–206 | DOI | MR | Zbl

[38] S. Tsynkov, S. Abarbanel, J. Nordström, V. Ryaben'kii, V. Vatsa, “Global artificial boundary conditions for computation of external flows with jets”, AIAA J., 38:11 (2000), 2014–2022 | DOI

[39] S. V. Tsynkov, Nelokalnye iskusstvennye granichnye usloviya dlya chislennogo resheniya zadach v neogranichennykh oblastyakh, Dis.\;...\;dokt. fiz.-matem. nauk, M., 2003, 217 pp.

[40] V. S. Ryaben'kii, “Faithful transfer of difference boundary conditions”, Funct. Anal. Appl., 24:3 (1990), 251–253 | DOI | MR | Zbl

[41] I. L. Sofronov, “Conditions for complete transparency on the sphere for the three-dimensional wave equation”, Russian Acad. Sci. Dokl. Math., 46:2 (1993), 397–401 | MR | Zbl

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[43] A. Dedner, D. Kröner, I. L. Sofronov, M. Wesenberg, “Transparent boundary conditions for MHD simulations in stratified atmospheres”, J. Comput. Phys., 171:2 (2001), 448–478 | DOI | Zbl

[44] J. Ballmann, G. Britten, I. Sofronov, “Time-accurate inlet and outlet conditions for unsteady transonic channel flow”, AIAA J., 40:9 (2002), 1745–1754 | DOI

[45] A. Arnold, M. Ehrhardt, I. Sofronov, “Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability”, Commun. Math. Sci., 1:3 (2003), 501–556 | DOI | MR | Zbl

[46] I. L. Sofronov, “O primenenii prozrachnykh granichnykh uslovii v zadachakh aeroakustiki”, Matem. modelirovanie, 19:8 (2007), 105–112 | Zbl

[47] N. A. Zaitsev, I. L. Sofronov, “Primenenie prozrachnykh granichnykh uslovii dlya resheniya dvumernykh zadach uprugosti s azimutalnoi anizotropiei”, Matem. modelirovanie, 19:8 (2007), 49–54 | MR | Zbl

[48] I. L. Sofronov, N. A. Zaitsev, “Numerical generation of transparent boundary conditions on the side surface of a vertical transverse isotropic layer”, J. Comput. Appl. Math., 234:6 (2010), 1732–1738 | DOI | MR | Zbl

[49] I. L. Sofronov, “Differential part of transparent boundary conditions for certain hyperbolic systems of second-order equations”, Dokl. Math., 79:3 (2009), 412–414 | DOI | MR | Zbl

[50] V. I. Turchaninov, “The gap phenomenon for solutions of the difference 3D-wave equation”, Dokl. Math., 62:3 (2000), 381 | MR | Zbl

[51] V. S. Ryabenkii, V. I. Turchaninov, S. V. Tsynkov, “Ispolzovanie lakun reshenii 3D-volnovogo uravneniya dlya vychisleniya resheniya na bolshikh vremenakh”, Matem. modelirovanie, 11:12 (1999), 113–126 | MR | Zbl

[52] V. S. Ryabenkii, V. I. Turchaninov, S. V. Tsynkov, “Neotrazhayuschie iskusstvennye granichnye usloviya dlya zameny otbrasyvaemykh uravnenii s lakunami”, Matem. modelirovanie, 12:12 (2000), 108–127 | MR | Zbl

[53] V. S. Ryaben'kii, S. V. Tsynkov, V. I. Turchaninov, “Long-time numerical computation of wave-type solutions driven by moving sources”, Appl. Numer. Math., 38:1-2 (2001), 187–222 | DOI | MR | Zbl

[54] V. S. Ryaben'kii, S. V. Tsynkov, V. I. Turchaninov, “Global discrete artificial boundary conditions for time-dependent wave propagation”, J. Comput. Phys., 174:2 (2001), 712–758 | DOI | MR | Zbl

[55] S. V. Tsynkov, “Artificial boundary conditions for the numerical simulation of unsteady acoustic waves”, J. Comput. Phys., 189:2 (2003), 626–650 | DOI | MR | Zbl

[56] S. V. Tsynkov, “On the application of lacunae-based methods to Maxwell's equations”, J. Comput. Phys., 199:1 (2004), 126–149 | DOI | MR | Zbl

[57] H. Qasimov, S. Tsynkov, “Lacunae based stabilization of PMLs”, J. Comput. Phys., 227:15 (2008), 7322–7345 | DOI | MR | Zbl

[58] E. T. Meier, A. H. Glasser, V. S. Lukin, U. Shumlak, “Modeling open boundaries in dissipative MHD simulation”, J. Comput. Phys., 231:7 (2012), 2963–2976 | DOI | MR | Zbl

[59] S. V. Petropavlovsky, S. V. Tsynkov, “Quasi-lacunae of Maxwell's equations”, SIAM J. Appl. Math., 71:4 (2011), 1109–1122 | DOI | MR | Zbl

[60] S. V. Petropavlovsky, S. V. Tsynkov, “A non-deteriorating algorithm for computational electromagnetism based on quasi-lacunae of Maxwell's equations”, J. Comput. Phys., 231:2 (2012), 558–585 | DOI | MR | Zbl

[61] V. S. Ryaben'kii, V. I. Turchaninov, Ye. Yu. Epshteyn, “Algorithm composition scheme for problems in composite domains based on the difference potential method”, Comput. Math. Math. Phys., 46:10 (2006), 1768–1784 | DOI | MR

[62] Y. Epshteyn, “Algorithms composition approach based on difference potentials method for parabolic problems”, Commun. Math. Sci., 12:4 (2014), 723–755 | DOI | MR | Zbl

[63] M. Medvinsky, S. Tsynkov, E. Turkel, “The method of difference potentials for the Helmholtz equation using compact high order schemes”, J. Sci. Comput., 53:1 (2012), 150–193 | DOI | MR | Zbl

[64] M. Medvinsky, S. Tsynkov, E. Turkel, “High order numerical simulation of the transmission and scattering of waves using the method of difference potentials”, J. Comput. Phys., 243 (2013), 305–322 | DOI | MR

[65] D. S. Britt, S. V. Tsynkov, E. Turkel, “A high-order numerical method for the Helmholtz equation with non-standard boundary conditions”, SIAM J. Sci. Comput., 35:5 (2013), A2255–A2292 | DOI | MR | Zbl

[66] S. Britt, S. Petropavlovsky, S. Tsynkov, E. Turkel, “Computation of singular solutions to the Helmholtz equation with high order accuracy”, Appl. Numer. Math., 93 (2015), 215–241 | DOI | MR | Zbl

[67] S. Britt, S. Tsynkov, E. Turkel, “Numerical simulation of time-harmonic waves in inhomogeneous media using compact high order schemes”, Commun. Comput. Phys., 9:3 (2011), 520–541 | DOI | MR

[68] E. Turkel, D. Gordon, R. Gordon, S. Tsynkov, “Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number”, J. Comput. Phys., 232:1 (2013), 272–287 | DOI | MR | Zbl

[69] Y. Epshteyn, S. Phippen, “High-order difference potentials methods for 1D elliptic type models”, Appl. Numer. Math., 93 (2015), 69–86 | DOI | MR | Zbl

[70] J. Albright, Y. Epshteyn, K. R. Steffen, “High-order accurate difference potentials methods for parabolic problems”, Appl. Numer. Math., 93 (2015), 87–106 | DOI | MR | Zbl

[71] V. S. Ryaben'kii, “Finite-difference shielding problem”, Funct. Anal. Appl., 29:1 (1995), 70–71 | DOI | MR | Zbl

[72] “Joint sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics and of the Moscow Mathematical Society (seventeenth session, 24–27 January 1995)”, Russian Math. Surveys, 50:4 (1995) | DOI

[73] R. I. Veĭtsman, V. S. Ryaben'kiĭ, “Difference problems of screening and imitation”, Dokl. Math., 55:3 (1997), 340–343 | MR | Zbl

[74] R. I. Veĭtsman, V. S. Ryaben'kiĭ, “Finite difference problems in simulation”, Trans. Moscow Math. Soc., 1997, 239–248 | MR | Zbl

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[76] J. Lončarić, V. S. Ryaben'kii, S. V. Tsynkov, “Active shielding and control of noise”, SIAM J. Appl. Math., 62:2 (2001), 563–596 | DOI | MR | Zbl

[77] V. S. Ryaben'kii, S. V. Utyuzhnikov, S. V. Tsynkov, “The problem of active noise shielding in composite domains”, Dokl. Math., 74:3 (2006), 812–814 | DOI | MR | Zbl

[78] V. S. Ryaben'kii, S. V. Tsynkov, S. V. Utyuzhnikov, “Inverse source problem and active shielding for composite domains”, Appl. Math. Lett., 20:5 (2007), 511–515 | DOI | MR | Zbl

[79] V. S. Ryaben'kii, S. V. Tsynkov, S. V. Utyuzhnikov, “Active control of sound with variable degree of cancellation”, Appl. Math. Lett., 22:12 (2009), 1846–1851 | DOI | MR | Zbl

[80] V. S. Ryaben'kii, “Use of weak noise for real-time control of strong noise suppression in a shielded subdomain”, Dokl. Math., 81:1 (2010), 137–138 | DOI | MR | Zbl

[81] A. W. Peterson, S. V. Tsynkov, “Active control of sound for composite regions”, SIAM J. Appl. Math., 67:6 (2007), 1582–1609 | DOI | MR | Zbl

[82] J. Lončarić, S. V. Tsynkov, “Optimization of acoustic source strength in the problems of active noise control”, SIAM J. Appl. Math., 63:4 (2003), 1141–1183 | DOI | MR | Zbl

[83] J. Lončarić, S. V. Tsynkov, “Optimization of power in the problems of active control of sound”, Math. Comput. Simulation, 65:4-5 (2004), 323–335 | DOI | MR | Zbl

[84] H. Lim, S. V. Utyuzhnikov, Y. W. Lam, A. Turan, M. R. Avis, V. S. Ryaben'kii, S. V. Tsynkov, “Experimental validation of the active noise control methodology based on difference potentials”, AIAA J., 47:4 (2009), 874–884 | DOI

[85] V. S. Ryaben'kii, “Real-time noise suppression in a three-dimensional protected subdomain as based on information from synchronous noise exploration”, Dokl. Math., 84:1 (2011), 562–564 | DOI | MR | Zbl

[86] V. S. Ryaben'kii, “Model of real-time active noise shielding of a given subdomain subject to external noise sources”, Comput. Math. Math. Phys., 51:3 (2011), 444–454 | DOI | MR | Zbl

[87] V. S. Ryaben'kii, “Synchronous exploration for the control of real-time external noise suppression in a three-dimensional subdomain”, Comput. Math. Math. Phys., 51:10 (2011), 1777–1791 | DOI | MR | Zbl

[88] V. S. Ryaben'kii, “Key information to control solutions of linear difference schemes in composite domains”, Dokl. Math., 85:3 (2012), 441–442 | DOI | MR | Zbl

[89] V. S. Ryaben'kii, “Mathematical model of devices used to suppress external noise in a subregion of space”, Math. Models Comput. Simul., 5:2 (2013), 103–121 | DOI | MR | Zbl

[90] V. S. Ryabenkii, V. I. Turchaninov, “Chislennye eksperimenty po upravleniyu podavleniem shuma v realnom vremeni”, Preprinty IPM im. M. V. Keldysha RAN (to appear)

[91] V. S. Ryabenkii, Vvedenie v vychislitelnuyu matematiku, Fizmatlit, M., 1994, 335 pp. ; 2-Рμ РёР·Рґ., 2000, 296 СЃ. ; 3-Рμ РёР·Рґ., 2008, 288 СЃ. | MR | Zbl | Zbl

[92] V. S. Ryaben'kii, S. V. Tsynkov, A theoretical introduction to numerical analysis, Chapman Hall/CRC, Boca Raton, FL, 2007, xiv+537 pp. | MR | Zbl

[93] V. D. Ivanov, V. I. Kosarev, A. I. Lobanov, I. B. Petrov, V. B. Pirogov, V. S. Ryabenkii, T. K. Starozhilova, A. G. Tormasov, S. V. Utyuzhnikov, A. S. Kholodov, Laboratornyi praktikum “Osnovy vychislitelnoi matematiki”, Ucheb. posobie MFTI, 2-e izd., ispr. i dop., MZ Press, M., 2003, 194 pp.

[94] V. S. Ryabenkii, Metod raznostnykh potentsialov i ego prilozheniya, 2-e izd., ispr. i dop., Fizmatlit, M., 2002, 494 pp. ; 3-Рμ РёР·Рґ., 2010, 432 СЃ.; V. S. Ryaben'kii, Method of difference potentials and its applications, Springer Ser. Comput. Math., 30, Springer-Verlag, Berlin, 2002, xviii+538 pp. | Zbl | DOI | MR | Zbl

[95] Appl. Numer. Math., 93, Special issue: International Conference “Difference Schemes and Applicatons” in honor of the 90-th birthday of Professor V. S. Ryaben'kii (2015), 1–294 | DOI