TY - JOUR

T1 - Fast domain decomposition type solver for stiffness matrices of reference p-elements

AU - Korneev, V.

PY - 2013

Y1 - 2013

N2 - A key component of domain decomposition solvers for hp discretizations of elliptic equations is the solver for internal stiffness matrices of p-elements. We consider an algorithm which belongs to the family of secondary domain decomposition solvers, based on the finite-difference like preconditioning of p-elements, and was outlined by the author earlier. We remove the uncertainty in the choice of the coarse (decomposition) grid solver and suggest the new interface Schur complement preconditioner. The latter essentially uses the boundary norm for discrete harmonic functions induced by orthotropic discretizations on slim rectangles, which was derived recently. We prove that the algorithm has linear arithmetical complexity.

AB - A key component of domain decomposition solvers for hp discretizations of elliptic equations is the solver for internal stiffness matrices of p-elements. We consider an algorithm which belongs to the family of secondary domain decomposition solvers, based on the finite-difference like preconditioning of p-elements, and was outlined by the author earlier. We remove the uncertainty in the choice of the coarse (decomposition) grid solver and suggest the new interface Schur complement preconditioner. The latter essentially uses the boundary norm for discrete harmonic functions induced by orthotropic discretizations on slim rectangles, which was derived recently. We prove that the algorithm has linear arithmetical complexity.

KW - Optimal Solvers

KW - Domain Decomposition Method

KW - p Finite Element Methods

KW - Solvers for Deteriorating Elliptic Equations

U2 - 10.1515/cmam-2013-0003

DO - 10.1515/cmam-2013-0003

M3 - Article

VL - 13

SP - 161

EP - 183

JO - Computational Methods in Applied Mathematics

JF - Computational Methods in Applied Mathematics

SN - 1609-4840

IS - 2

ER -