V. G. Korneev, S. A. Ivanov, “Preconditioning in the domain decomposition methods for the $p$-version with the hierarchical bases”, Mat. Model., 8:9 (1996), 63

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Matematicheskoe modelirovanie, 1996, Volume 8, Number 9, Pages 63–73 (Mi mm1620)

This article is cited in 5 scientific papers (total in 5 papers)

Proceedins of the International Conference on the Optimization of the Finite Element Approximations (OFEA-95), St.-Petersburg, 25–29 June 1995

Preconditioning in the domain decomposition methods for the

$p$ -version with the hierarchical bases

V. G. Korneev, S. A. Ivanov

Russian Center of Laser Physics, Research Institute of St. Petersburg State University

Full-text PDF (1107 kB) Citations (5)

Abstract: A DD (domain decomposition) method is considered for the

$p$ - and

$h$ -

$p$ -versions with the curvilinear elements for the elliptic second order partial differential equation. Coordinate functions of the reference element are defined by the products of the Legendre's polynomials. Efficient DD preconditioner is suggested on the basis of preconditioners for the problems on subdomains and for the Shur complement.

Bibliographic databases:

Language: English

Citation: V. G. Korneev, S. A. Ivanov, “Preconditioning in the domain decomposition methods for the

$p$ -version with the hierarchical bases”, Mat. Model., 8:9 (1996), 63–73

Citation in format AMSBIB

\Bibitem{KorIva96}

\by V.~G.~Korneev, S.~A.~Ivanov

\paper Preconditioning in the domain decomposition methods for the $p$-version with the hierarchical bases

\jour Mat. Model.

\yr 1996

\vol 8

\issue 9

\pages 63--73

\mathnet{http://mi.mathnet.ru/mm1620}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1444873}

\zmath{https://zbmath.org/?q=an:0981.65512}

Linking options:

https://www.mathnet.ru/eng/mm1620

https://www.mathnet.ru/eng/mm/v8/i9/p63

This publication is cited in the following 5 articles:

Korneev, V, “Fast domain decomposition algorithm discretizations of 3-d elliptic equations by spectral elements”, Computer Methods in Applied Mechanics and Engineering, 197:17–18 (2008), 1433
Comput. Math. Math. Phys., 47:10 (2007), 1656–1674
I. E. Anufriev, V. G. Korneev, “Numerical testing of a decomposition method for the $p$ -version of the finite element method”, Russian Math. (Iz. VUZ), 49:1 (2005), 7–20
V. G. Korneev, J. E. Flaherty, T. Oden, J. Fish, “ $hp$ -version additive Schwarz algorithms on triangular meshes”, Matem. modelirovanie, 14:2 (2002), 61–94
V. G. Korneev, “Local Dirichlet problems on subdomains of decomposition in $HP$ -discretizations, and optimal algorithms for their solution”, Matem. modelirovanie, 14:5 (2002), 51–74

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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