Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
SIAM Journal on Numerical Analysis
An Additive Schwarz Method for the h-b Version of the Finite Element Method in Three Dimensions
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
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In this paper, we propose to modify a preconditioner developed in Pavarino and Widlund (Comput. Math. Appl. 33 (1997) 193) for three-dimensional p-version finite element or spectral element approximations by solving the sub-problems on element faces with an inexact element face solver. Such a modification reduces the cost to evaluate the action of the preconditioner from O(p4) to O(p3) per element face, where p is the polynomial degree used for approximation. Furthermore, it is shown that the coefficient matrix of the inexact solver is spectrally equivalent to the original stiffness matrix on element faces. Therefore, such a change will not affect the polylogarithmic estimate given in Pavarino and Widlund for the condition number of the preconditioned system. Numerical results are also given to confirm the theoretical analysis.