The paper covers the development and research of mathematical models of «bloom» phytoplankton processes, that cause hypoxic phenomena in shallow waters, on the basis of modern information technologies and computational methods. Expedition data and multichannel satellite images of remote sensing obtained by the SRC «Planet» are used for calibration and verification of the developed model. The methods of domain decomposition was used in a parallel implementation for computationally labours problems, taking into account the architecture and parameters of multiprocessor computer system.

Domain decomposition method based on adjoint equation and inverse problem theory is discussed. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. The splitting method is used for time approximations. Domain decomposition method is studied to convection-diffusion problem. Also using domain decomposition method on multiprocessor computer system is possible to create algorithms for the parallel calculations.

Algorithms for solving the Navier-Stokes equations on a three-dimensional tetrahedral grid by the discontinuous Galerkin method were realized. Under the code development a new approach to programming problems of mathematical physics was used which allows one compactly write and effectively implement mathematical expressions in particular due to introduction of the concept of «grid operator» similar to mathematical one and uniformly realize algorithms for various grid types and computing architectures. The efficiency of this numerical code is investigated.

Algorithms are proposed to study the sensitivity of the optimal solution to the errors of the observational data in the problem of variational assimilation of the sea surface temperature data with the aim of restoring heat fluxes for the nonstationary system of thermodynamic equations. Numerical experiments are presented in an application to the model of the thermodynamics of the Baltic Sea.

The problem of numerical modeling of the process of initiation of seismic activity on Arctic shelf and its impact on engineering structures is considered. To describe the dynamic behavior of a geological array, the determining systems of equations of the theory of elasticity and acoustics are used with explicit identification of all geological layers. A distinctive feature of the developed approach is the full wave calculation of the propagation of seismic waves from the source of the earthquake to the day surface. Grid-characteristic method is used for numerical calculation on hexahedral and tetrahedral computational grids.

The article is devoted to the investigation of difference schemes for equations of convectiondiffusion type. Such equations are widely used in the description of non-linear processes. In this
paper we consider a spatially one-dimensional variant, although the main features of the equation are retained here: nonmonotonicity and quasilinearity.
The purposes of the work were the development and calculation of flux schemes with a double exponential transformation. This paper presents the results of constructing and generalizing conservative weakly monotonic schemes of second-order accuracy on space on uniform and quasiuniform grids. A generalization of the proposed schemes to the case of the use of cellular meshes
was performed.

The paper describes several approaches to adaptation of Cartesian grids in fluid and gasdynamics problems. It is demonstrated that the filter based on non-uniform B-splines is more appropriate for this class of problems.

The paper considers an approach to detection of buildings and structures in the satellite imagery. The proposed method performs the extraction of high objects in a digital surface model and then improves the recognition accuracy using the segmentation of spectral information. The results of the quality comparison of the proposed approach with using different image segmentation algorithms are presented.

The paper covers the architecture and main functional components of the basic system of modelling (BSM), as the integrated high-performance computational environment to solve interdisciplinary direct and inverse problems on the multi- processor computational system (MPS) with distributed and shared hierarchical memory. BSM subsystems support the stages of geometric and functional modelling, grid generation, high order approximations, fast algebraic solutions, etc. The scalable parallelism is provided by means of hybrid programming models: MPI, OpenMP, computational libraries for graphic accelerators and vectorization. The BSM main principles are discussed to have wide applications and long life cycle.