Solution of Assimilation Observation Data Problem for Shallow Water Equations for SMP-Nodes Cluster

Karepova, E.; Dementyeva, Ekaterina

doi:10.1007/978-3-642-23178-0_39

Cited by 1 publication

(7 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The bilinear form a(Φ, W) and the linear forms b(d, W), f (W) have been presented in [2,9,11,12]. Note that boundary conditions (1.2) are natural for problem (1.1), i.e., do not pose any requirements on the spaces of test functions.…”

Section: De Nition 21 the Vector Functionmentioning

confidence: 98%

“…Here and below the functions are given along the east boundary corresponding to λ = . • E. We present the results of the reconstruction of the boundary function d in the following three di erent spaces: L (Γ ), W (Γ ), and W / (Γ ) (see also [11,12]). …”

Section: Problemmentioning

confidence: 99%

“…Write in Ω the following momentum and energy equations discretized in time [2,11,12] for the unknown…”

Section: Inverse Problem For a Boundary Functionmentioning

confidence: 99%

“…In [11], the boundary function was reconstructed in the space L (Γ ) and in [6,12] this was done in the space W (Γ ) of greater smoothness, which allowed one to use fewer observation data for its reconstruction, or use noised data. Using the necessary Euler optimality condition for the target functional proposed here, we reduce the solution of the inverse problem to an iterative process consisting in a sequential solution of direct and adjoint problems using the equation for improvement of the required boundary function.…”

Section: Mscmentioning

confidence: 99%

“…An additional information concerning the solution is used in this case and a quality functional corresponding to the considered problem is de ned. The original inverse problem in this case is reduced to minimization of the introduced functional.This paper continues the series of papers [2,11,12] considering the iterative algorithm for reconstruction of an unknown boundary function d from observation data where this function describes the in uence of the ocean through the open boundary Γ of the calculation domain. The inverse problem is posed after the discretization in time of the initial boundary value problem simulating the propagation of surface waves in large water areas subject to the Earth sphericity and Coriolis acceleration on the base of the motion and continuity equations averaged over the vertical direction.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Assimilation of observation data in the problem of surface wave propagation in a water area with an open boundary

Дементьева

Karepova

Shaidurov

2014

Russian Journal of Numerical Analysis and Mathematical Modelling

View full text Add to dashboard Cite

An iterative algorithm for reconstruction of an unknown boundary function from observation data in the space of traces W / (Γ ) is considered in the paper for the case of a function describing the in uence of the ocean through an open boundary of the calculation domain. The algorithm has been tested on a model problem for the Sea of Okhotsk.Keywords: Surface waves propagation models, inverse problem for a boundary function, ill-posed problems, nite element method. MSC: 65R32, 74J15, 76B15 Ekaterina V. Dement'eva, Eugeniya D. Karepova, Vladimir V. Shaidurov: Institute of Computational Modelling, Siberian Branch of the RAS, 660036 Krasnoyarsk, RussiaVarious topics of mathematical and numerical modelling of tidal ows and surface waves in large water areas have been considered in [2,7,14,15]. In order to determine solutions to such problems uniquely, the values of certain input parameters (characterizing the properties of the medium) and also initial and boundary functions should be speci ed in those models. However, some parameters or functions may be unknown in practice and we have to determine them using some additional information concerning the solution, i.e., to solve an inverse problem. In most cases such problems are ill-posed and hence we have to use appropriate methods especially aimed at solving ill-posed problems.One of the approaches to solving ill-posed inverse problems in mathematical physics is based on the use of optimal control methods [1,3,8,17]. An additional information concerning the solution is used in this case and a quality functional corresponding to the considered problem is de ned. The original inverse problem in this case is reduced to minimization of the introduced functional.This paper continues the series of papers [2,11,12] considering the iterative algorithm for reconstruction of an unknown boundary function d from observation data where this function describes the in uence of the ocean through the open boundary Γ of the calculation domain. The inverse problem is posed after the discretization in time of the initial boundary value problem simulating the propagation of surface waves in large water areas subject to the Earth sphericity and Coriolis acceleration on the base of the motion and continuity equations averaged over the vertical direction.As the result, we solve an ill-posed inverse problem for a boundary function at each time step and introduce a stabilizing term into the quality functional according to the method of Tikhonov; this term depends on the space where we seek for this boundary function. In [11], the boundary function was reconstructed in the space L (Γ ) and in [6,12] this was done in the space W (Γ ) of greater smoothness, which allowed one to use fewer observation data for its reconstruction, or use noised data. Using the necessary Euler optimality condition for the target functional proposed here, we reduce the solution of the inverse problem to an iterative process consisting in a sequential solution of direct and adjoint problems using the equation for improv...

show abstract

Section: De Nition 21 the Vector Functionmentioning

confidence: 98%

Section: Problemmentioning

confidence: 99%

“…Write in Ω the following momentum and energy equations discretized in time [2,11,12] for the unknown…”

Section: Inverse Problem For a Boundary Functionmentioning

confidence: 99%

Section: Mscmentioning

confidence: 99%

mentioning

confidence: 99%