This paper describes a new algorithm to solve the neutron transport stationary equation in 2-D geometry. This algorithm is based on a splitting of the collision operator and an infinite dimensional adaptation of the G...
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This paper describes a new algorithm to solve the neutron transport stationary equation in 2-D geometry. This algorithm is based on a splitting of the collision operator and an infinite dimensional adaptation of the gmres method accelerated by a symmetric Gauss-Seidel preconditioning. The theoretical proof of the convergence and the numerical results are given in this work.
The PageRank algorithm for determining the importance of Web pages has become a central technique in Web search. we propose a new method to speed up the convergence performance for computing PageRank when the damping ...
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The PageRank algorithm for determining the importance of Web pages has become a central technique in Web search. we propose a new method to speed up the convergence performance for computing PageRank when the damping factor is close to one, called as gmres-Power, which is based on a periodic combination of the power method with the gmres algorithm. The description and convergence analysis of the new algorithm are discussed in detail. Numerical results are reported to confirm the efficiency of the new algorithm. (C) 2018 Elsevier B.V. All rights reserved.
Krylov subspace methods are commonly used iterative methods for solving large sparse linear systems. However, they suffer from communication bottlenecks on parallel computers. Therefore, s-step methods have been devel...
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Krylov subspace methods are commonly used iterative methods for solving large sparse linear systems. However, they suffer from communication bottlenecks on parallel computers. Therefore, s-step methods have been developed, where the Krylov subspace is built block by block so that s matrix-vector multiplications can be done before orthonormalizing the block. Then Communication-Avoiding algorithms can be used for both kernels. This paper introduces a new variation on the s-step gmres method in order to reduce the number of iterations necessary to ensure convergence with a small overhead in the number of communications. Namely, we develop an s-step gmres algorithm, where the block size is variable and increases gradually. Our numerical experiments show a good agreement with our analysis of condition numbers and demonstrate the efficiency of our variable s-step approach.
The Robin iteration procedure is a technique for the FEM computation of electromagnetic scattering fields in unbounded domains. It is based on the iterative improvement of the known term of a non-homogeneous Robin con...
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The Robin iteration procedure is a technique for the FEM computation of electromagnetic scattering fields in unbounded domains. It is based on the iterative improvement of the known term of a non-homogeneous Robin condition on a fictitious boundary enclosing the scatterer. In this paper it is shown that the procedure is equivalent to the application of the Richardson method to a reduced system and that the use of gmres significantly reduces the computational effort.
We show to what extent the accuracy of the inner products computed in the gmres iterative solver can be reduced as the iterations proceed without affecting the convergence rate or final accuracy achieved by the iterat...
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We show to what extent the accuracy of the inner products computed in the gmres iterative solver can be reduced as the iterations proceed without affecting the convergence rate or final accuracy achieved by the iterates. We bound the loss of orthogonality in gmres with inexact inner products. We use this result to bound the ratio of the residual norm in inexact gmres to the residual norm in exact gmres and give a condition under which this ratio remains close to 1. We illustrate our results with examples in variable floating-point arithmetic.
A solver is developed for time-accurate computations of viscous flows based on the conception of Newton's method.A set of pseudo-time derivatives are added into governing equations and the discretized system is so...
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A solver is developed for time-accurate computations of viscous flows based on the conception of Newton's method.A set of pseudo-time derivatives are added into governing equations and the discretized system is solved using gmres *** to some special properties of gmres algorithm,the solution procedure for unsteady flows could be regarded as a kind of Newton *** physical-time derivatives of governing equations are discretized using two different approaches,i.e.,3-point Euler backward,and Crank-Nicolson formulas,both with 2nd-order accuracy in time but with different truncation *** turbulent eddy viscosity is calculated by using a version of Spalart-Allmaras one-equation model modified by authors for turbulent *** cases of unsteady viscous flow are investigated to validate and assess the solver,i.e.,low Reynolds number flow around a row of cylinders and transonic bi-circular-arc airfoil flow featuring the vortex shedding and shock buffeting problems,***,comparisons between the two schemes of timederivative discretizations are carefully *** is illustrated that the developed unsteady flow solver shows a considerable efficiency and the Crank-Nicolson scheme gives better results compared with Euler method.
A mathematical program is proposed for the highly nonlinear problem involving frictional contact. A program-pattern using the fast multipole boundary element method (FM- BEM) is given for 3-D elastic contact with fric...
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A mathematical program is proposed for the highly nonlinear problem involving frictional contact. A program-pattern using the fast multipole boundary element method (FM- BEM) is given for 3-D elastic contact with friction to replace the Monte Carlo method. A new optimized generalized minimal residual (gmres) algorithm is presented. Numerical examples demonstrate the validity of the program-pattern optimization model for node-to-surface contact with friction. The gmres algorithm greatly improves the computational efciency.
Computational fluid dynamics (CFD) is used extensively by engineers to model and analyze complex issues related to hydraulic design, planning studies for future generating stations, civil maintenance and supply effici...
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Computational fluid dynamics (CFD) is used extensively by engineers to model and analyze complex issues related to hydraulic design, planning studies for future generating stations, civil maintenance and supply efficiency. In order to find the optimal position of a baffle in a rectangular primary sedimentation tank, computational investigations are performed. Also laboratory experiments are conducted to verify the numerical results and the measured velocity fields which were by Acoustic Doppler Velocimeter (ADV) are used. The gmres algorithm as a pressure solver was used in the computational modeling. The results of computational investigations performed in the present study indicate that the favorable flow field (uniform in the settling zone) would be enhanced for the case that the baffle position provide small circulation regions volume and dissipate the kinetic energy in the tank. Also results show that the gmres algorithm can obtain the good agreement between the results of numerical models and experimental tests. (C) 2012 Elsevier Inc. All rights reserved.
In this paper we propose and analyse some algorithms for solving block linear systems which are based upon the block Gram-Schmidt method. In particular, we prove that the algorithm BCGS2 (Reorthogonalized Block Classi...
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In this paper we propose and analyse some algorithms for solving block linear systems which are based upon the block Gram-Schmidt method. In particular, we prove that the algorithm BCGS2 (Reorthogonalized Block Classical Gram-Schmidt) using Householder Q-R decomposition implemented in floating-point arithmetic is backward stable, under the mild assumptions. Numerical tests were done in MATLAB to illustrate our theoretical results. A particular emphasis is on symmetric saddle-point problems, which arise in many important practical applications. We compare the results with the generalized minimal residual (gmres) algorithm.
We propose a method of Lanczos type for solving a linear system with a normal matrix whose spectrum is contained in a second-degree curve. This is a broader class of matrices than that of the (l, m)-normal matrices in...
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We propose a method of Lanczos type for solving a linear system with a normal matrix whose spectrum is contained in a second-degree curve. This is a broader class of matrices than that of the (l, m)-normal matrices introduced in a recent paper by Barth and Manteuffel. Our approach is similar to that of Huhtanen in the sense that both use the condensed form of normal matrices discovered by Elsner and Ikramov. However, there are a number of differences, among which are: (i) our method is modeled after the SYMMLQ algorithm of Paige and Saunders;(11) it uses only one matrix-vector product per step;(iii) we provide effective means for monitoring the size of the residual during the process. Numerical experiments are presented.
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