Research output: Chapter in Book/Report/Conference proceeding › Article in an anthology › Research
Fast Domain Decomposition Algorithms for Discretizations of 3-d Elliptic Equations by Spectral Elements. / Korneev, V.; Rytov, A.
Domain Decomposition Methods in Science and Engineering XVII. Springer Nature, 2008. p. 559-565 (Lecture Notes in Computational Science and Engineering; Vol. 60).Research output: Chapter in Book/Report/Conference proceeding › Article in an anthology › Research
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TY - CHAP
T1 - Fast Domain Decomposition Algorithms for Discretizations of 3-d Elliptic Equations by Spectral Elements
AU - Korneev, V.
AU - Rytov, A.
N1 - Korneev, V., Rytov, A. (2008). Fast Domain Decomposition Algorithms for Discretizations of 3-d Elliptic Equations by Spectral Elements. In: Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75199-1_70
PY - 2008
Y1 - 2008
N2 - The main obstacle for obtaining fast domain decomposition solvers for the spectral element discretizations of the 2-nd order elliptic equations was absence of fast solvers for the internal problems on subdomains of decomposition and their faces. It was shown by Korneev/Rytov (2005) that such solvers can be derived on the basis of the specific interrelation between the stiffness matrices of the spectral and hierarchical $p$ reference elements. The coordinate polynomials of the latter are produced by the tensor products of the integrated Legendre's polynomials. This interrelation allows to apply to the spectral element discretizations fast solvers which in some basic features are quite similar to those developed for the discretizations by the hierarchical elements. Using these facts, we present the almost optimal in the arithmetical cost domain decomposition preconditioner-solver for the spectral element discretizations of the 2-nd order elliptic equations in 3-$d$ domains.
AB - The main obstacle for obtaining fast domain decomposition solvers for the spectral element discretizations of the 2-nd order elliptic equations was absence of fast solvers for the internal problems on subdomains of decomposition and their faces. It was shown by Korneev/Rytov (2005) that such solvers can be derived on the basis of the specific interrelation between the stiffness matrices of the spectral and hierarchical $p$ reference elements. The coordinate polynomials of the latter are produced by the tensor products of the integrated Legendre's polynomials. This interrelation allows to apply to the spectral element discretizations fast solvers which in some basic features are quite similar to those developed for the discretizations by the hierarchical elements. Using these facts, we present the almost optimal in the arithmetical cost domain decomposition preconditioner-solver for the spectral element discretizations of the 2-nd order elliptic equations in 3-$d$ domains.
KW - domain decomposition
KW - spectral element discretizations
KW - fast solvers
KW - preconditioning.
UR - https://link.springer.com/book/10.1007/978-3-540-75199-1
M3 - Article in an anthology
SN - 978-3-540-75198-4
T3 - Lecture Notes in Computational Science and Engineering
SP - 559
EP - 565
BT - Domain Decomposition Methods in Science and Engineering XVII
PB - Springer Nature
ER -
ID: 4589976