Тезисы докладов

Доклады новосибирских участников

The problems of research and development of computational technologies for mathematical modeling of wide class of processes and phenomena are considered. The corresponding mathematical statements are supposed to be described by the systems of partial differential and/or integral equation or by equivalent variational formulations, including multi-dimensional and multi-model problems (linear or nonlinear, stationary or nonstationary). The optimal control problems are included in consideration also what means the directed multi-variant computations under modifications of geometrical or functional input data of original parametrized problem. The conception is based on the implementation of modern numerical approaches with using unstructured adapted grids, domain decomposition and multigrid methods, which demands an efficicial program tools and data structures for automatical construction of such high level intellegent algorithms. The instrument for solution of a such questions is considered as the system of geometrical and functional modeling (SGFM) which is presented as a set of paradigms and definitions, program tools and data structures. This system is constructed as problem oriented but application independent in the sense that it can be used via its back-front for different particular applied program packages (APPs). The set of geometrical classes consists of points, curves, segments, surfaces, subdomains and some standard figures which are served for description of computational domains. Each object is provided by its specifications, properties, admissible operations and reciprocal relations with other objects. The typical geometrical operations are the computing of intersections of curves and/or surfaces, the localization of points, the definition of subdomains and modifications: shifting, rotation and scaling of various components, as well as creation, supplementation and deleting of objects. The closure of mathematical statement includes the description of the systems of equations and its coefficients, in principle different ones for different subdomains, and boundary or initial conditions, connected with different parts of boundaries of computational domain. Functional data can include also the descriptions of algorithms to be used and scenario of computational experiment. For solution of optimal control problems, each item of input data can be parametrized and supplied by the bounds for parameters, in terms of inequalities or equalities. Such problems are supplied also by the descriptions of cost functions and functional constraints. The conventional approach for solution of minimization or inverse problem is presented as directed sequental multivariant solutions of direct problems. Such SGFM must be provided by the flexible geometrical data structure and functional data structure (GDS and FDS), in other to ensure the compatible graphic user interface and internal intrface with computational moduls. Different configurations can be used as essential component of particular APPs or as instrument for development of research or training mathematical software.

Дополнительные материалы:

PDF (722 kb)

Примечание. Тезисы докладов публикуются в авторской редакции

Ваши комментарии Обратная связь

[Головная страница] [Конференции]

© 1996-2001, Институт вычислительных технологий СО РАН, Новосибирск
© 1996-2001, Сибирское отделение Российской академии наук, Новосибирск