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In this note, we compare some Krylov subspace iterative methods on the MASPAR, a massively parallel computer with 16K processors. In particular, we apply these methods to solve large sparse nonsymmetric linear systems arising from elliptic partial differential equations. The methods under consideration include conjugate gradient type methods, semiiterative methods, and a hybrid variant. Our numerical results show that, on the MASPAR, one should compare iterative methods rather on the basis of total...
An algorithm of the preconditioned conjugate gradient method in which the solution of an auxiliary system is replaced with multiplication by the matrix for suitably chosen is presented.
Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the...
In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.
We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...
We consider linear elliptic systems which arise
in coupled elastic continuum mechanical models. In these systems, the strain
tensor εP := sym (P-1∇u) is redefined to include a
matrix valued inhomogeneity P(x) which cannot be described by a space
dependent fourth order elasticity tensor. Such systems arise naturally in
geometrically exact plasticity or in problems with eigenstresses.
The tensor field P induces a structural change of the elasticity equations. For
such a model the FETI-DP method is...
The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
The present paper deals with a finite element approximation of partial differential equations when the
domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming
because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized.
We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
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