Speaker
Prof.
Vasily Shapeev
(Novosibirsk National Research University, Novosibirsk, Russia, Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia)
Description
In the numerical method of collocations and the least residuals (CLR),
the boundary differential problem using the collocation method is
projected into a finite-dimensional linear functional space. To find the
solution of the obtained approximate problem, an overdetermined system
of linear algebraic equations (SLAE) is written out and it is required
that on its solution the minimum of the discrepancy functional of all
its equations is attained. From this requirement and the presence of a
piecewise analytic solution of the approximate problem, a number of
merits of the method follows. In particular, the algorithms of the CLR
method are relatively simple to apply in non-canonical regions and on
irregular grids. It is relatively simple to build variants of the method
of increased accuracy, including those for sufficiently ill-conditioned
problems and with singularities in the solution of the initial
differential problem. Its algorithms are easily parallelized. In the CLR
method, modern algorithms of computational mathematics are effectively
used: multigrid complexes, Krylov subspaces, preconditioners, irregular
grids. The presented report will give a brief overview of the latest
results obtained in the CLR method and demonstrate its indicated
properties.
Primary author
Prof.
Vasily Shapeev
(Novosibirsk National Research University, Novosibirsk, Russia Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia)
