Relevant bibliographies by topics / Preconditioned Krylov subspace method

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Academic literature on the topic 'Preconditioned Krylov subspace method'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Preconditioned Krylov subspace method"

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Gryazin, Yury. "Preconditioned Krylov Subspace Methods for Sixth Order Compact Approximations of the Helmholtz Equation." ISRN Computational Mathematics 2014 (January 21, 2014): 1–15. http://dx.doi.org/10.1155/2014/745849.

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We consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann, and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and lower order preconditioned Krylov subspace methodology. The resulting systems of finite-difference equations are solved by different preconditioned Krylov subspace-based methods. In the analysis of the lower order preconditioning developed here, we introduce the term “kth order preconditioned matrix” in addition to the commonly used “an optimal preconditioner.” The necessity of the
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Liu, Jia. "An Alternative HSS Preconditioner for the Unsteady Incompressible Navier-Stokes Equations in Rotation Form." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/307939.

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We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the Krylov subspace-iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, Reynolds numbers, time step, and algorithm parameters. The preconditioner is efficient and easy to apply for the unsteady Oseen problems in rotation form.
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Chen, Dandan, Ting-Zhu Huang, and Liang Li. "Comparison of Algebraic Multigrid Preconditioners for Solving Helmholtz Equations." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/367909.

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An algebraic multigrid (AMG) with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation (DPA) scheme firstly proposed by Y. Notay (2006) as the coarsening method. We compare it with the smoothed aggregation algebraic multigrid and meanwhile show shifted Laplacian preconditioners. According to numerical r
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Huang, Yunying, and Guoliang Chen. "A relaxed block splitting preconditioner for complex symmetric indefinite linear systems." Open Mathematics 16, no. 1 (2018): 561–73. http://dx.doi.org/10.1515/math-2018-0051.

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AbstractIn this paper, we propose a relaxed block splitting preconditioner for a class of complex symmetric indefinite linear systems to accelerate the convergence rate of the Krylov subspace iteration method and the relaxed preconditioner is much closer to the original block two-by-two coefficient matrix. We study the spectral properties and the eigenvector distributions of the corresponding preconditioned matrix. In addition, the degree of the minimal polynomial of the preconditioned matrix is also derived. Finally, some numerical experiments are presented to illustrate the effectiveness of
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Zheng, Zhong, and Guo Feng Zhang. "A Block Diagonal Preconditioner for Generalised Saddle Point Problems." East Asian Journal on Applied Mathematics 6, no. 3 (2016): 235–52. http://dx.doi.org/10.4208/eajam.260815.280216a.

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AbstractA lopsided alternating direction iteration (LADI) method and an induced block diagonal preconditioner for solving block two-by-two generalised saddle point problems are presented. The convergence of the LADI method is analysed, and the block diagonal preconditioner can accelerate the convergence rates of Krylov subspace iteration methods such as GMRES. Our new preconditioned method only requires a solver for two linear equation sub-systems with symmetric and positive definite coefficient matrices. Numerical experiments show that the GMRES with the new preconditioner is quite effective.
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Oliveira, Suely, and Yuanhua Deng. "Preconditioned Krylov subspace methods for transport equations." Progress in Nuclear Energy 33, no. 1-2 (1998): 155–74. http://dx.doi.org/10.1016/s0149-1970(97)00099-1.

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Chan, T. F., E. Chow, Y. Saad, and M. C. Yeung. "Preserving Symmetry in Preconditioned Krylov Subspace Methods." SIAM Journal on Scientific Computing 20, no. 2 (1998): 568–81. http://dx.doi.org/10.1137/s1064827596311554.

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Li, Cheng-Liang, and Chang-Feng Ma. "On Euler preconditioned SHSS iterative method for a class of complex symmetric linear systems." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 5 (2019): 1607–27. http://dx.doi.org/10.1051/m2an/2019029.

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In this paper, we propose an Euler preconditioned single-step HSS (EP-SHSS) iterative method for solving a broad class of complex symmetric linear systems. The proposed method can be applied not only to the non-singular complex symmetric linear systems but also to the singular ones. The convergence (semi-convergence) properties of the proposed method are carefully discussed under suitable restrictions. Furthermore, we consider the acceleration of the EP-SHSS method by preconditioned Krylov subspace method and discuss the spectral properties of the corresponding preconditioned matrix. Numerical
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Hu, Zixiang, Shi Zhang, Yun Zhang, Huamin Zhou, and Dequn Li. "An efficient preconditioned Krylov subspace method for large-scale finite element equations with MPC using Lagrange multiplier method." Engineering Computations 31, no. 7 (2014): 1169–97. http://dx.doi.org/10.1108/ec-03-2013-0077.

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Purpose – The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method. Design/methodology/approach – In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compa
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Vuik, C. "Krylov Subspace Solvers and Preconditioners." ESAIM: Proceedings and Surveys 63 (2018): 1–43. http://dx.doi.org/10.1051/proc/201863001.

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In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved. Fast solution of these systems is very urgent nowadays. The size of the problems can be 1013 unknowns and 1013 equations. Iterative solution methods are the methods of choice for these large linear systems. We start with a short introduction of Basic Iterative Methods. Thereafter preconditioned Krylov subspace methods, which are state of the art, are describeed. A distinction is
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Dissertations / Theses on the topic "Preconditioned Krylov subspace method"

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Du, Xiuhong. "Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG." Diss., Temple University Libraries, 2008. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/6474.

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Mathematics<br>Ph.D.<br>The GMRES method is a widely used iterative method for solving the linear systems, of the form Ax = b, especially for the solution of discretized partial differential equations. With an appropriate preconditioner, the solution of the linear system Ax = b can be achieved with less computational effort. Additive Schwarz Preconditioners have two good properties. First, they are easily parallelizable, since several smaller linear systems need to be solved: one system for each of the sub-domains, usually corresponding to the restriction of the differential operator to that s
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Ahuja, Kapil. "Recycling Krylov Subspaces and Preconditioners." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/29539.

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Science and engineering problems frequently require solving a sequence of single linear systems or a sequence of dual linear systems. We develop algorithms that recycle Krylov subspaces and preconditioners from one system (or pair of systems) in the sequence to the next, leading to efficient solutions. Besides the benefit of only having to store few Lanczos vectors, using BiConjugate Gradients (BiCG) to solve dual linear systems may have application-specific advantages. For example, using BiCG to solve the dual linear systems arising in interpolatory model reduction provides a backward err
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Pestana, Jennifer. "Nonstandard inner products and preconditioned iterative methods." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:2e5b636b-1145-461e-80fa-ea2041ec476f.

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By considering Krylov subspace methods in nonstandard inner products, we develop in this thesis new methods for solving large sparse linear systems and examine the effectiveness of existing preconditioners. We focus on saddle point systems and systems with a nonsymmetric, diagonalizable coefficient matrix. For symmetric saddle point systems, we present a preconditioner that renders the preconditioned saddle point matrix nonsymmetric but self-adjoint with respect to an inner product and for which scaling is not required to apply a short-term recurrence method. The robustness and effectiveness o
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Liang, Qiao. "Singular Value Computation and Subspace Clustering." UKnowledge, 2015. http://uknowledge.uky.edu/math_etds/30.

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In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an in
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Liu, Jun. "NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS." OpenSIUC, 2015. https://opensiuc.lib.siu.edu/dissertations/1076.

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Partial differential equations are the chief means of providing mathematical models in science, engineering and other fields. Optimal control of partial differential equations (PDEs) has tremendous applications in engineering and science, such as shape optimization, image processing, fluid dynamics, and chemical processes. In this thesis, we develop and analyze several efficient numerical methods for the optimal control problems governed by elliptic PDE, parabolic PDE, and wave PDE, respectively. The thesis consists of six chapters. In Chapter 1, we briefly introduce a few motivating applicati
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Moufawad, Sophie. "Enlarged Krylov Subspace Methods and Preconditioners for Avoiding Communication." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066438/document.

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La performance d'un algorithme sur une architecture donnée dépend à la fois de la vitesse à laquelle le processeur effectue des opérations à virgule flottante (flops) et de la vitesse d'accès à la mémoire et au disque. Etant donné que le coût de la communication est beaucoup plus élevé que celui des opérations arithmétiques, celle-là forme un goulot d'étranglement dans les algorithmes numériques. Récemment, des méthodes de sous-espace de Krylov basées sur les méthodes 's-step' ont été développées pour réduire les communications. En effet, très peu de préconditionneurs existent pour ces méthode
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Lei, Siu Long. "Some applications of Krylov subspace methods with circulant-type preconditioners." Thesis, University of Macau, 2000. http://umaclib3.umac.mo/record=b1446687.

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Badahmane, Achraf. "Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres." Thesis, Littoral, 2019. http://www.theses.fr/2019DUNK0543.

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La résolution numérique des problèmes de point-selle a eu une attention particulière ces dernières années. À titre d'exemple, la mécanique des fluides et solides conduit souvent à des problèmes de point-selle. Ces problèmes se présentent généralement par des équations aux dérivées partielles que nous linéarisons et discrétisons. Le problème linéaire obtenu est souvent mal conditionné. Le résoudre par des méthodes itératives standard n'est donc pas approprié. En plus, lorsque la taille du problème est grande, il est nécessaire de procéder par des méthodes de projections. Nous nous intéressons d
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Moulin, Johann. "On the flutter bifurcation in laminar flows : linear and nonlinear modal methods." Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAX093.

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L'instabilité de flottement a été le sujet de nombreuses études depuis le milieu du vingtième siècle à cause de ses applications critiques en aéronautique. Elle est classiquement décrite comme un instabilité linéaire en écoulement potentiel, mais les effets visqueux et nonlinéaires du fluide peuvent avoir un impact crucial.La première partie de cette thèse est consacrée au développement de méthodes théoriques et numériques pour l'analyse linéaire et nonlinéaire de la dynamique d'une ``section typique aéroélastique'' --- une plaque montée sur des ressorts de flexion et torsion --- plongée dans
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Li, Ming. "Recycling Preconditioners for Sequences of Linear Systems and Matrix Reordering." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/64382.

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In science and engineering, many applications require the solution of a sequence of linear systems. There are many ways to solve linear systems and we always look for methods that are faster and/or require less storage. In this dissertation, we focus on solving these systems with Krylov subspace methods and how to obtain effective preconditioners inexpensively. We first present an application for electronic structure calculation. A sequence of slowly changing linear systems is produced in the simulation. The linear systems change by rank-one updates. Properties of the system matrix are analyz
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Books on the topic "Preconditioned Krylov subspace method"

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Amini, S. Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation. University of Salford Department of Mathematics and Computer Science, 1995.

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Preserving symmetry in preconditioned Krylov subspace methods. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1996.

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F, Chan Tony, and Research Institute for Advanced Computer Science (U.S.), eds. Preserving symmetry in preconditioned Krylov subspace methods. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1996.

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F, Chan Tony, and Research Institute for Advanced Computer Science (U.S.), eds. Preserving symmetry in preconditioned Krylov subspace methods. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1996.

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F, Chan Tony, and Research Institute for Advanced Computer Science (U.S.), eds. Preserving symmetry in preconditioned Krylov subspace methods. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1996.

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Book chapters on the topic "Preconditioned Krylov subspace method"

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Saad, Youcef. "Supercomputer Implementations of Preconditioned Krylov Subspace Methods." In Algorithmic Trends in Computational Fluid Dynamics. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-2708-3_8.

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Meister, Andreas, and Christof Vömel. "Preconditioned krylov subspace methods for Hyperbolic conservation laws." In Hyperbolic Problems: Theory, Numerics, Applications. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8372-6_24.

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Saad, Yousef. "Preconditioned Krylov Subspace Methods for the Numerical Solution of Markov Chains." In Computations with Markov Chains. Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-2241-6_4.

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Chen, Zejun, and Hong Xiao. "Preconditioned Krylov Subspace Methods Solving Dense Nonsymmetric Linear Systems Arising from BEM." In Computational Science – ICCS 2007. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-72588-6_16.

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Ilin, Valery P. "Multi-preconditioned Domain Decomposition Methods in the Krylov Subspaces." In Lecture Notes in Computer Science. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57099-0_9.

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Tadano, Hiroto, and Tetsuya Sakurai. "On Single Precision Preconditioners for Krylov Subspace Iterative Methods." In Large-Scale Scientific Computing. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78827-0_83.

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Jain, Vidushi, and Yogesh Nagor. "Krylov Subspace Method Using Quantum Computing." In Advances in Intelligent Systems and Computing. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-9927-9_27.

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Ju, Jianwei, and Giovanni Lapenta. "Predictor-Corrector Preconditioned Newton-Krylov Method For Cavity Flow." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11428831_11.

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Morigi, Serena, Lothar Reichel, and Fiorella Sgallari. "A Cascadic Alternating Krylov Subspace Image Restoration Method." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38267-3_9.

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Tan, Sheldon, Mehdi Tahoori, Taeyoung Kim, Shengcheng Wang, Zeyu Sun, and Saman Kiamehr. "Fast EM Stress Evolution Analysis Using Krylov Subspace Method." In Long-Term Reliability of Nanometer VLSI Systems. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26172-6_3.

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Conference papers on the topic "Preconditioned Krylov subspace method"

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Shaw, Scott, and Ning Qin. "A matrix-free preconditioned Krylov-subspace method for the PNS equations." In 36th AIAA Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics, 1998. http://dx.doi.org/10.2514/6.1998-111.

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Ikuno, Soichiro, Gong Chen, Taku Itoh, Susumu Nakata, and Kuniyoshi Abe. "Variable preconditioned Krylov subspace method with communication avoiding technique for electromagnetic analysis." In 2016 IEEE Conference on Electromagnetic Field Computation (CEFC). IEEE, 2016. http://dx.doi.org/10.1109/cefc.2016.7816153.

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Carpentieri, Bruno. "Preconditioned Krylov subspace methods for solving high-frequency cavity problems in electromagnetics." In 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC). IEEE, 2015. http://dx.doi.org/10.1109/ursi-at-rasc.2015.7302942.

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Chen, Tsung-Hao, and Charlie Chung-Ping Chen. "Efficient large-scale power grid analysis based on preconditioned krylov-subspace iterative methods." In the 38th conference. ACM Press, 2001. http://dx.doi.org/10.1145/378239.379023.

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Ikuno, Soichiro, and Taku Itoh. "GPU acceleration of variable preconditioned Krylov subspace method for linear system obtained by eXtended element-free Galerkin method." In 2017 IEEE International Conference on Computational Electromagnetics (ICCEM). IEEE, 2017. http://dx.doi.org/10.1109/compem.2017.7912804.

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Wang, Mianzhi, and Chia-fon F. Lee. "Efficient Computation Methods for Combustion Reaction Kinetics." In ASME 2014 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icef2014-5648.

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This research presents multiple strategies to improve the computation efficiency of solving combustion reaction kinetics. All strategies in this work are error-free compared to other methods based on result tabulation, dynamic mechanism reduction, and stiffness removal with quasi-equilibrium assumption and lower-dimensional manifold attraction. In the presented methods, the Jacobian matrix are solved by either direct linear solver or preconditioned Krylov subspace method. Different Jacobian matrix construction methods are designed with exploiting the characteristics of reaction network. The me
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Ianculescu, Cristian, and Lonny L. Thompson. "Parallel Iterative Methods for the Helmholtz Equation With Exact Nonreflecting Boundaries." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32744.

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Parallel iterative methods for fast solution of large-scale acoustic radiation and scattering problems are developed using exact Dirichlet-to-Neumann (DtN), nonreflecting boundaries. A separable elliptic nonreflecting boundary is used to efficiently model unbounded regions surrounding elongated structures. We exploit the special structure of the non-local DtN map as a low-rank update of the system matrix to efficiently compute the matrix-by-vector products found in Krylov subspace based iterative methods. For the complex non-hermitian matrices resulting from the Helmholtz equation, we use a di
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Lukyanov, A., J. van der Linden, T. B. Jönsthövel, and C. Vuik. "Meshless Subdomain Deflation Vectors in the Preconditioned Krylov Subspace Iterative Solvers." In ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery. EAGE Publications BV, 2014. http://dx.doi.org/10.3997/2214-4609.20141773.

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de Sturler, Eric, Chau Le, Shun Wang, et al. "Large Scale Topology Optimization Using Preconditioned Krylov Subspace Recycling and Continuous Approximation of Material Distribution." In MULTISCALE AND FUNCTIONALLY GRADED MATERIALS 2006. AIP, 2008. http://dx.doi.org/10.1063/1.2896790.

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Imakura, Akira, Tetsuya Sakurai, Kohsuke Sumiyoshi, and Hideo Matsufuru. "An Auto-Tuning Technique of the Weighted Jacobi-Type Iteration Used for Preconditioners of Krylov Subspace Methods." In 2012 IEEE 6th International Symposium on Embedded Multicore Socs (MCSoC). IEEE, 2012. http://dx.doi.org/10.1109/mcsoc.2012.29.

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Reports on the topic "Preconditioned Krylov subspace method"

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Freund, R. W., and N. M. Nachtigal. A new Krylov-subspace method for symmetric indefinite linear systems. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/10190810.

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