We study a 2-level multiplicative Schwarz method for the p version Galerkin boundary element method for a weakly singular integral equation of the first kind in 3D. We prove that the rate of convergence of the multipl...
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We study a 2-level multiplicative Schwarz method for the p version Galerkin boundary element method for a weakly singular integral equation of the first kind in 3D. We prove that the rate of convergence of the multiplicative Schwarz operator for the p version grows only logarithmically in p and is independent of h. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.
In this paper we propose a superfast implementation of Wilson's method for the spectral factorization of Laurent polynomials based on a preconditioned conjugate gradient algorithm. The new computational scheme fol...
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ISBN:
(纸本)0819445584
In this paper we propose a superfast implementation of Wilson's method for the spectral factorization of Laurent polynomials based on a preconditioned conjugate gradient algorithm. The new computational scheme follows by exploiting several recently established connections between the considered factorization problem and the solution of certain discrete-time Lyapunov matrix equations whose coefficients are in controllable canonical form. The results of many numerical experiments even involving polynomials of very high degree are reported and discussed by showing that our preconditioning strategy is quite effective just when starting the iterative phase with a roughly approximation of the sought factor. Thus, our approach provides an efficient refinement procedure which is particularly suited to be combined with linearly convergent factorization algorithms when suffering from a very slow convergence due to the occurrence of roots close to the unit circle.
We study a multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method with geometrically graded meshes. Both hypersingular and weakly singular integral equations of the first kind a...
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We study a multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method with geometrically graded meshes. Both hypersingular and weakly singular integral equations of the first kind are considered. As it is well known the h-p version with geometric meshes converges exponentially fast in the energy-norm. However, the condition number of the Galerkin matrix in this case blows up exponentially in the number of unknowns M. We prove that the condition number kappa(P) of the multilevel additive Schwarz operator behaves like O(root Mlog(2) M). Asa direct consequence of this we also give the results for the 2-level preconditioner and also for the h-p version with quasi-uniform meshes. Numerical results supporting our theory are presented.
A preconditionedconjugategradient (PCG)-based domain decomposition method was given in [11] and [12] for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem....
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