Mathematical modeling by application of spline functions
The laboratory of the theory of spline functions carries out the research
in processing an experimental information, based on the spline theory and
its applications. In many practical problems an initial information is represented
by the values of multivariate functions which are known (usually approximately
with some error) in arbitrary scattered on the plane or in the space points.
The number of points can be very large (thousands or tens of thousands).
To solve the problem of fitting a function to a set of arbitrary scattered
data the conception of Multistage Method was developed. The essence of the
method is contents in splitting of the approximation process into a number
of stages and combining splines, specially intended for the data on arbitrary
grids (Dm-splines, Hardy type interpolation
and their generalizations) and splines on rectangular grids (cubic splines
and there modifications).
To process a 2-dimensional geophysics information there
was created a software product.
Later to process the results of hydraulic turbine energetic tests there
were created an interactive of high fidelity software products YX (the
hill diagram for Frances turbine and YHPL (the hill diagram for Kaplan
turbine, which are successfully employed at the Joint-Stock Company "Leningradsky
Metallichesky Zavod".
The production of modern systems for automated design (CAD) and manufacturing
(CAM) complex-shaped items such as airfoils of wing or fuselage of air
crafts, hulls of ships, vanes of hydraulic and gas turbine is inconceivable
without splines. Just those problems gave an initial impetus for beginning
the research on splines at the Sobolev Institute of Mathematics under
guidance of Professor Yu. S. Zavyalov in the 60's. There were
developed a number of effective methods of approximation to the curves
and surfaces by parametric splines. On this base a software product ASTRA
was created. It is intended to support geometrically the process of automated
design and technological preparation for the manufacturing articles, which
have complex spatial contours. ASTRA is a multi-purpose system and it
can be adapted to various tasks.
It was put into operation on a number of factories in Russia (Novosibirsk
Aviation Production Association named after Valery Chkalov and Joint-Stock
Company "Leningradsky Metallichesky Zavod") The scientists of
the laboratory: Yu. S. Zavyalov, V. A. Leus, and V. A. Skorospelov
together with the employees of the Chkalov Novosibirsk Aircraft Production
Assotiation were awarded the Prise of the USSR Counsil of Ministers in
1981 for large contribution into development of new technologies in aircraft
production.
