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Математические заметки, 2022, том 112, выпуск 6, статья опубликована в англоязычной версии журнала
(Mi mzm13824)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Статьи, опубликованные в английской версии журнала
The Method of Harmonic Mapping of Regions with a Notch
S. I. Bezrodnykha, V. I. Vlasovba a Federal Research Center "Computer Science and Control"
of Russian Academy of Sciences, Moscow, 119333 Russia
b Moscow Center for Fundamental and Applied Mathematics,
Moscowб 119991 Russia
Аннотация:
It is well known that common numerical methods
encounter serious computational difficulties
when constructing harmonic mappings of regions
with notches and generating computational
grids in such regions on the basis of these mappings.
We propose an efficient computational technique for
constructing a harmonic mapping of domains with a
rectangular notch based on the analytical–numerical
multipole method.
Our research demonstrates high
computational efficiency of the proposed method;
the use of only $40$
approximative functions
(multipoles) provides an error
of less than $10^{-7}$ in the
$C (\overline{g})$ norm.
The
result is obtained with the help of a posteriori
estimation.
We find a condition ensuring that the grid line
issuing from the vertex of an angle of magnitude
$\pi \beta$,
$\beta >1$, is not tangent to the angle sides
at this vertex, which prevents the emergence of an
adverse grid self-overlapping effect.
Ключевые слова:
harmonic mapping, narrow notch domain,
conformal mapping, analytical-numerical multipole
method.
Поступило: 25.08.2022 Исправленный вариант: 20.09.2022
Образец цитирования:
S. I. Bezrodnykh, V. I. Vlasov, “The Method of Harmonic Mapping of Regions with a Notch”, Math. Notes, 112:6 (2022), 831–844
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mzm13824
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Страница аннотации: | 112 |
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