TY - GEN

T1 - Solving discrete dirichlet problems on spectral finite elements by fast domain decomposition algorithm

AU - Korneev, Vadim Glebovich

PY - 2014

Y1 - 2014

N2 - A key component of DD (domain decomposition) solvers for hp discretizations of elliptic equations is the solver for the internal stiffness matrices of p-elements. We consider the algorithm of the linear complexity for solving such problems on spectral p-elements, which, therefore, in the leading DD solver plays the role of the second stage DD solver. It is based on the first order finite element preconditioning of the Orszag type for the reference element stiffness matrices. Earlier, for spectral elements, only fast solvers obtained with the use of special preconditioners in factored form were known. The most intricate part of the algorithm is the inter-subdomain Schur complement preconditioning by inexact iterative solver employing two preconditioners -- preconditioner-solver and preconditioner-multiplicator. From general point of view, the solver developed in the paper is the DD solver for the discretization on a strongly variable in size and shape deteriorating mesh with the number of subdomains growing with the growth of the number of degrees of freedom.

AB - A key component of DD (domain decomposition) solvers for hp discretizations of elliptic equations is the solver for the internal stiffness matrices of p-elements. We consider the algorithm of the linear complexity for solving such problems on spectral p-elements, which, therefore, in the leading DD solver plays the role of the second stage DD solver. It is based on the first order finite element preconditioning of the Orszag type for the reference element stiffness matrices. Earlier, for spectral elements, only fast solvers obtained with the use of special preconditioners in factored form were known. The most intricate part of the algorithm is the inter-subdomain Schur complement preconditioning by inexact iterative solver employing two preconditioners -- preconditioner-solver and preconditioner-multiplicator. From general point of view, the solver developed in the paper is the DD solver for the discretization on a strongly variable in size and shape deteriorating mesh with the number of subdomains growing with the growth of the number of degrees of freedom.

KW - Fast solvers

KW - Preconditioning

KW - Schur complement preconditioning

KW - Spectral finite elements

UR - http://www.scopus.com/inward/record.url?scp=84905020734&partnerID=8YFLogxK

U2 - 10.4028/www.scientific.net/AMM.587-589.2312

DO - 10.4028/www.scientific.net/AMM.587-589.2312

M3 - Conference contribution

SN - 9783038351672

T3 - Applied Mechanics and Materials

SP - 2312

EP - 2329

BT - Sustainable Cities Development and Environment Protection IV

PB - Trans Tech Publications Ltd

T2 - 4th International Conference on Civil Engineering, Architecture and Building Materials, CEABM 2014

Y2 - 24 May 2014 through 25 May 2014

ER -