Developing Structural Methods For Solving Boundary-Value Problems In Non-Smooth Boundary Domains
Вантажиться...
Дата
2016
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
NTU "KhPI"
Анотація
The paper presents the development of structural methods for solving boundary-value problems in complexshape
domains to enhance calculation accuracy in the neighbourhood of angular points in the boundary-value
problems solution domain.
Structural methods allow building bases for solving mathematical physics boundary-value problems, which
accurately account for the boundary conditions and geometric information on the domain form. These methods
are based on using the mathematical tools of the theory of R-functions. They can dramatically extend the
potentialities of variation methods when solving mathematical physics boundary-value problems in complexshape
domains with different boundary conditions.
The most common systems of R-operations used in practice are normalised; however, they are not smooth in
point (0,0), and all smooth R-operations are not normalised.
The paper presents the results of investigating the behaviour of smooth functions up to the domain boundary,
which satisfy uniform Dirichlet and Neumann conditions, and the condition at which the function proper and its
derivatives over the normal to a definite order are equal to zero. New approaches are offered to build basis
functions that are smooth up to the non-smooth domain boundary and which meet the above-mentioned
boundary conditions.
The suggested new system of asymptotically normalised R-operations whose functions belong to the given
smoothness class can be used to build smooth basis functions that satisfy certain boundary conditions.
The approaches developed were tested for model problems, some of which were used for problems in modelling
hydrodynamic fields in complex-shape domains.
Опис
Ключові слова
Бібліографічний опис
Baranov I. Developing Structural Methods For Solving Boundary-Value Problems In Non-Smooth Boundary Domains / I. Baranov, O. Kravchenko, I. Suvorova // Nonlinear Dynamics–2016 (ND-KhPI2016) : proceedings of 5th International Conference, dedicated to the 90th anniversary of Academician V. L. Rvachev, September 27-30, 2016 = Нелінійна динаміка–2016 : тези доп. 5-ї Міжнар. конф., 27-30 вересня 2016 р. – Kharkov : NTU "KhPI", 2016. – P. 416.