A series of studies have been made on the development of methods for investigating and numerical solving the quasilinear data assimilation problems, based on the adjoint equation theory, optimal control methods, and perturbation algorithms. The data assimilation problems are formulated as optimal control problems for the models governed by quasilinear evolution equations with the aim to identify the initial data and/or the right-hand-side (source)functions of the original equations. The neccessary optimality condition reduces the problem under consideration to the optimality system involving the original evolution problem, the adjoint problem, and the optimality condition (the last means that the Gateaux derivative of the cost functional equals zero). For linearized problem, by eliminating the state and adjoint variables, the optimality system is reduced to the only equation for the unknown function to be identified (the control function). This control equation has the form Lu=F, where L is a linear operator (called the control operator), u is the sought-for function, and the right-hand side F is determined by the input data. The properties of the control operators were studied, which are often symmetric, non-negative and compact. Based on the properties of the control operators, the solvability of linear and nonlinear data assimilation problems in a specific functional spaces is proved. To study the solvability of nonlinear data assimilation problems the successive approximation method is used. Using the spectral properties of the control operators, various iterative algorithms for solving the data assimilation problems are formulated and justified with optimal choice of iteration parameters. The convergence rate estimates are derived. The main results of this series are published in the author's book "Control operators and iterative algorithms in variational data assimilation problems (Moscow: Nauka, 2001).
Biography
Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University in 1979. Ph.D. thesis was defended in 1983. D.Sci. thesis was defended in 1999.
Member of GAMM (Gesellschaft fur Angewandte Mathematik und Mechanik).
Main publications:
Marchuk G. I., Agoshkov V. I., Shutyaev V. I. Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. New York: CRC Press, 1996. 275 p. (izdano v Rossii: M.: Nauka, 1993).
Shutyaev V. P. Operatory upravleniya i iteratsionnye algoritmy v zadachakh variatsionnogo usvoeniya dannykh. M.: Nauka, 2001. 239 s.
Shutyaev V. P. Ob usvoenii dannykh v shkale gilbertovykh prostranstv dlya kvazilineinykh evolyutsionnykh zadach // Differentsialnye uravneniya, 1998, 34(3), 383–389.
Shutyaev V. P. Iteratsionnye metody vosstanovleniya nachalnykh dannykh v singulyarno vozmuschennykh evolyutsionnykh zadachakh // ZhVM i MF, 1997, 37(9), 1078–1086.
Shutyaev V. P. O svoistvakh operatora upravleniya v odnoi zadache ob usvoenii dannykh i algoritmakh ee resheniya // Matematicheskie zametki, 1995, 57(6), 941–944.
V. P. Shutyaev, E. I. Parmuzin, “Sensitivity of functionals to input data in a variational assimilation problem for the sea thermodynamics model”, Sib. Zh. Vychisl. Mat., 27:1 (2024), 97–112
2023
2.
V. P. Dymnikov, D. V. Kulyamin, P. A. Ostanin, V. P. Shutyaev, “Data assimilation for the two-dimensional ambipolar diffusion equation in Earth’s ionosphere model”, Zh. Vychisl. Mat. Mat. Fiz., 63:5 (2023), 803–826; Comput. Math. Math. Phys., 63:5 (2023), 845–867
3.
E. I. Parmuzin, V. P. Shutyaev, “Sensitivity of functionals of the solution to the variational assimilation problem to the input data on the heat flux for a model of sea thermodynamics”, Zh. Vychisl. Mat. Mat. Fiz., 63:4 (2023), 657–666; Comput. Math. Math. Phys., 63:4 (2023), 623–632
V. P. Shutyaev, E. I. Parmuzin, “Sensitivity of functionals of the solution of a variational
data assimilation problem with simultaneous reconstruction of heat fluxes and the initial state
for the sea thermodynamics model”, Sib. Zh. Vychisl. Mat., 23:4 (2020), 457–470; Num. Anal. Appl., 13:4 (2020), 382–392
2019
5.
V. P. Shutyaev, E. I. Parmuzin, “Sensitivity of functionals to observation data in a variational assimilation problem for the sea thermodynamics model”, Sib. Zh. Vychisl. Mat., 22:2 (2019), 229–242; Num. Anal. Appl., 12:2 (2019), 191–201
V. P. Shutyaev, E. I. Parmuzin, “Stability of the optimal solution to the problem of variational assimilation with error covariance matrices of observational data for the sea thermodynamics model”, Sib. Zh. Vychisl. Mat., 21:2 (2018), 225–242; Num. Anal. Appl., 11:2 (2018), 178–192
G. I. Marchuk, V. P. Shutyaev, “Adjoint equations and iterative algorithms in problems of variational data assimilation”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:2 (2011), 136–150; Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S138–S152
V. I. Agoshkov, E. I. Parmuzin, V. P. Shutyaev, “Numerical algorithm for variational assimilation of sea surface temperature data”, Zh. Vychisl. Mat. Mat. Fiz., 48:8 (2008), 1371–1391; Comput. Math. Math. Phys., 48:8 (2008), 1293–1312
V. P. Shutyaev, “On the solvability of an initial-boundary value problem for a quasilinear heat equation”, Differ. Uravn., 35:6 (1999), 809–812; Differ. Equ., 35:6 (1999), 811–814
10.
I. Yu. Gejadze, V. P. Shutyaev, “An optimal control problem of initial data restoration”, Zh. Vychisl. Mat. Mat. Fiz., 39:9 (1999), 1479–1488; Comput. Math. Math. Phys., 39:9 (1999), 1416–1425
V. P. Shutyaev, “On data assimilation in a scale of Hilbert spaces for quasilinear evolution problems”, Differ. Uravn., 34:3 (1998), 383–389; Differ. Equ., 34:3 (1998), 382–388
I. Yu. Gejadze, V. P. Shutyaev, “Substantiation of the perturbation method for a quasilinear heat-conduction problem”, Zh. Vychisl. Mat. Mat. Fiz., 38:6 (1998), 948–955; Comput. Math. Math. Phys., 38:6 (1998), 909–915
1997
13.
V. P. Shutyaev, “Iterative method for initial-data reconstruction in singularly perturbed evolutionary problems”, Zh. Vychisl. Mat. Mat. Fiz., 37:9 (1997), 1078–1086; Comput. Math. Math. Phys., 37:9 (1997), 1042–1050
14.
E. I. Parmuzin, V. P. Shutyaev, “Algorithms for solving a problem of data assimilation”, Zh. Vychisl. Mat. Mat. Fiz., 37:7 (1997), 816–827; Comput. Math. Math. Phys., 37:7 (1997), 792–803
V. P. Shutyaev, “Some properties of a control operator in the problem of data assimilation, and algorithms for its solution”, Differ. Uravn., 31:12 (1995), 2063–2069; Differ. Equ., 31:12 (1995), 2035–2041
V. P. Shutyaev, “The properties of control operators in one problem on data control and algorithms for its solution”, Mat. Zametki, 57:6 (1995), 941–944; Math. Notes, 57:6 (1995), 668–671
V. P. Shutyaev, “Properties of a solution of a conjugate equation in a nonlinear hyperbolic problem”, Differ. Uravn., 28:4 (1992), 706–715; Differ. Equ., 28:4 (1992), 577–585
1991
19.
V. P. Shutyaev, “Perturbation method for a weakly nonlinear hyperbolic first order problem”, Mat. Zametki, 50:5 (1991), 156–158; Math. Notes, 50:5 (1991), 1207–1208
20.
V. P. Shutyaev, “Justification of perturbation algorithm in a nonlinear hyperbolic problem”, Mat. Zametki, 49:4 (1991), 155–156; Math. Notes, 49:4 (1991), 439–440
21.
V. P. Shutyaev, “Computation of a functional in a certain nonlinear problem using the adjoint equation”, Zh. Vychisl. Mat. Mat. Fiz., 31:9 (1991), 1278–1288; U.S.S.R. Comput. Math. Math. Phys., 31:9 (1991), 8–16
Sensitivity and error propagation in a variational framework F.-X. Le Dimet, V. P. Shutyaev, T. H. Tran Междкнародная конференция, посвященная 90-летию со дня рождения Г. И. Марчука "Современные проблемы вычислительной математики и математического моделирования" June 9, 2015 11:00
2.
О работах Г. И. Марчука в области вычислительной математики и ее приложений V. I. Agoshkov, V. B. Zalesnyi, V. P. Shutyaev Междкнародная конференция, посвященная 90-летию со дня рождения Г. И. Марчука "Современные проблемы вычислительной математики и математического моделирования" June 8, 2015 17:30
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