Конференции ИВТ СО РАН

MIT-2009
Международная конференция "Математические и информационные технологии"
(VIII конференция "Вычислительные и информационные технологии в науке, технике и образовании")

Копаоник, Сербия, 27 - 31 августа 2009 года;
Будва, Черногория, 31 августа - 5 сентября 2009 года

Тезисы докладов

Методы и технологии решения междисциплинарных прямых и обратных волновых задач

Ильин В.П.

ИВМиМГ СО РАН (Новосибирск)

The computational methods and technologies are considered for solving interdiscipline direct and inverse wave problems which arise in various applications:elasticity,acoustics, electromagnetics,etc. The initial-boundary value problems in classical differential statements and equivalent variational formulations for generalized solutions are approximated by means of compact finite difference methods (FDM),finite volume methods (FVM),and finite element methods (FEM), with vector and scalar basic functions of different types and orderes at the structured and non-structured grids. The spectral approaches based on Fourier,or Laguerre,or Laplace transforms are analysed and compared also. The stability conditions and convergence properties as well as computational complexity of different algorithms are investigated. The structural and spectral peculiarities of obtained systems of linear algebraic equations (SLAE) for each time steps of implicit schemes are discussed. The set of solvers for symmetric and non-symmetric SLAEs with large sparse positive definite or indefinite matrices are applied on the base of preconditioned iterative processes in Krylov subspaces. The conception of unified instrumental software kernel,to support the different computational stages,is presented.It includes geometrical and functional modeling,the libraries of grid generators, approximators and algebraic solvers as well as optimization algorithms for solution of the inverse problems. The requirements for high performance of parallel algorithms and its efficient mapping at the multi-processor and multi-core computer architectures with shared and distributed memory are discussed.The example of implemented applied program package for the fast modeling of the 3D electromanetic vector fields in frequency domain is described.

Примечание. Тезисы докладов публикуются в авторской редакции

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