TY - JOUR

T1 - Fast domain decomposition algorithm discretizations of 3-d elliptic equations by spectral elements

AU - Korneev, V.

AU - Rytov, A.

PY - 2008

Y1 - 2008

N2 - The main obstacle for obtaining fast domain decomposition solvers for spectral element discretizations of 2-nd order elliptic equations was the lack of fast solvers for local internal problems on subdomains of decomposition and their faces. As recently shown by Korneev/Rytov, such solvers can be derived on the basis of a specific interrelation between stiffness matrices of the spectral and hierarchical p reference elements (coordinate polynomials of the latter are tensor products of the integrated Legendre’s polynomials). This interrelation allows us to develop fast solvers for discretizations by spectral elements, which are quite similar in basic features to those developed for discretizations by hierarchical elements. Using these facts and preceding findings on the wire basket preconditioners, we present a domain decomposition preconditioner-solver for spectral element discretizations of 2-nd order elliptic equations in 3-d domains which is almost optimal in the total arithmetical cost.

AB - The main obstacle for obtaining fast domain decomposition solvers for spectral element discretizations of 2-nd order elliptic equations was the lack of fast solvers for local internal problems on subdomains of decomposition and their faces. As recently shown by Korneev/Rytov, such solvers can be derived on the basis of a specific interrelation between stiffness matrices of the spectral and hierarchical p reference elements (coordinate polynomials of the latter are tensor products of the integrated Legendre’s polynomials). This interrelation allows us to develop fast solvers for discretizations by spectral elements, which are quite similar in basic features to those developed for discretizations by hierarchical elements. Using these facts and preceding findings on the wire basket preconditioners, we present a domain decomposition preconditioner-solver for spectral element discretizations of 2-nd order elliptic equations in 3-d domains which is almost optimal in the total arithmetical cost.

KW - Domain decomposition

KW - Spectral element discretizations

KW - Fast solvers

KW - Preconditioning

U2 - doi:10.1016/j.cma.2007.10.013

DO - doi:10.1016/j.cma.2007.10.013

M3 - Article

VL - 197

SP - 1433

EP - 1446

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 17-18

ER -