Substructuring Preconditioner for Nonconforming Finite Element Approximations of Second Order Elliptic Problems with Anisotropy
نویسنده
چکیده
Abstract In this paper an algebraic substructuring preconditioner is considered for nonconforming nite element approximations of second order elliptic problems in D domains with diagonal anisotropic di usion tensor Using a block Gauss elimination and a substructuring idea part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent matrix When the domain considered is a parallelepiped and boundary conditions are uniform on entire faces this matrix is separable Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner It is shown that the condition number of the preconditioned matrix does not depend neither on meshsize parameter nor on the coe cients of the di usion tensor The numerical experiments show that proposed preconditioner is rather e cient and can be used for development of iteration solvers for general elliptic equations of second order on domains topologically equivalent to a parallelepiped
منابع مشابه
Substructuring Preconditioner for Nonconforming Finite Element Approximations of Second Order Elliptic Problems with Anisotropy
Abstract In this paper an algebraic substructuring preconditioner is considered for nonconforming nite element approximations of second order elliptic problems in D domains with diagonal anisotropic di usion tensor Using a block Gauss elimination and a substructuring idea part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent matrix Whe...
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