Relevant bibliographies by topics / Conjugate Residual method

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Conjugate Residual method'

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Published: 6 September 2023
Last updated: 7 September 2023

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Journal articles on the topic "Conjugate Residual method"

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Dahito, Marie-Ange, and Dominique Orban. "The Conjugate Residual Method in Linesearch and Trust-Region Methods." SIAM Journal on Optimization 29, no. 3 (January 2019): 1988–2025. http://dx.doi.org/10.1137/18m1204255.

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Axelsson, Owe, and M. Makarov. "On a generalized conjugate gradient orthogonal residual method." Numerical Linear Algebra with Applications 2, no. 5 (September 1995): 467–79. http://dx.doi.org/10.1002/nla.1680020507.

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Ogino, Masao, Shin-ichiro Sugimoto, Seigo Terada, Yanqing Bao, and Hiroshi Kanayama. "A Large-Scale Magnetostatic Analysis Using an Iterative Domain Decomposition Method Based on the Minimal Residual Method." Journal of Advanced Computational Intelligence and Intelligent Informatics 16, no. 4 (June 20, 2012): 496–502. http://dx.doi.org/10.20965/jaciii.2012.p0496.

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This paper describes a large-scale 3D magnetostatic analysis using the Domain Decomposition Method (DDM). To improve the convergence of the interface problem of DDM, a DDM approach based on the Conjugate Residual (CR) method or the MINimal RESidual (MINRES) method is proposed. The CR or MINRES method improved the convergence rate and showed more stable convergence behavior in solving the interface problem than the Conjugate Gradient (CG) method, and reduced computation time for a large-scale problem with about 10 million degrees of freedom.
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Li, Tao, Qing-Wen Wang, and Xin-Fang Zhang. "A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations." Mathematics 10, no. 10 (May 18, 2022): 1730. http://dx.doi.org/10.3390/math10101730.

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This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving the tensor equations. A theoretical analysis shows that the proposed method converges to an exact solution for any initial tensor at most finite steps in the absence round-off errors. Compared with a modified conjugate gradient method, the obtained numerical results illustrate that our methods perform much better in terms of the number of iteration steps and computing time.
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Washizawa, Teruyoshi. "On the Behavior of the Residual in Conjugate Gradient Method." Applied Mathematics 01, no. 03 (2010): 211–14. http://dx.doi.org/10.4236/am.2010.13025.

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Gurieva, Y. L. "Semi-conjugate residual method for iterative solving the Navier-Stokes problem." Optoelectronics, Instrumentation and Data Processing 43, no. 2 (April 2007): 177–81. http://dx.doi.org/10.3103/s8756699007020100.

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EGUCHI, Yuzuru, Laszlo FUCHS, and Genki YAGAWA. "A finite element analysis of unsteady flows utilizing conjugate residual method." Transactions of the Japan Society of Mechanical Engineers Series A 53, no. 485 (1987): 111–15. http://dx.doi.org/10.1299/kikaia.53.111.

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Sogabe, T., M. Sugihara, and S. L. Zhang. "An extension of the conjugate residual method to nonsymmetric linear systems." Journal of Computational and Applied Mathematics 226, no. 1 (April 2009): 103–13. http://dx.doi.org/10.1016/j.cam.2008.05.018.

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Toh, Kim-Chuan, and Masakazu Kojima. "Solving Some Large Scale Semidefinite Programs via the Conjugate Residual Method." SIAM Journal on Optimization 12, no. 3 (January 2002): 669–91. http://dx.doi.org/10.1137/s1052623400376378.

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Zhong, Hong-Xiu, Xian-Ming Gu, and Shao-Liang Zhang. "A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides." Symmetry 11, no. 10 (October 16, 2019): 1302. http://dx.doi.org/10.3390/sym11101302.

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The block conjugate orthogonal conjugate gradient method (BCOCG) is recognized as a common method to solve complex symmetric linear systems with multiple right-hand sides. However, breakdown always occurs if the right-hand sides are rank deficient. In this paper, based on the orthogonality conditions, we present a breakdown-free BCOCG algorithm with new parameter matrices to handle rank deficiency. To improve the spectral properties of coefficient matrix A, a precondition version of the breakdown-free BCOCG is proposed in detail. We also give the relative algorithms for the block conjugate A-orthogonal conjugate residual method. Numerical results illustrate that when breakdown occurs, the breakdown-free algorithms yield faster convergence than the non-breakdown-free algorithms.
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Dissertations / Theses on the topic "Conjugate Residual method"

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Odland, Tove. "On Methods for Solving Symmetric Systems of Linear Equations Arising in Optimization." Doctoral thesis, KTH, Optimeringslära och systemteori, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-166675.

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In this thesis we present research on mathematical properties of methods for solv- ing symmetric systems of linear equations that arise in various optimization problem formulations and in methods for solving such problems. In the first and third paper (Paper A and Paper C), we consider the connection be- tween the method of conjugate gradients and quasi-Newton methods on strictly convex quadratic optimization problems or equivalently on a symmetric system of linear equa- tions with a positive definite matrix. We state conditions on the quasi-Newton matrix and the update matrix such that the search directions generated by the corresponding quasi-Newton method and the method of conjugate gradients respectively are parallel. In paper A, we derive such conditions on the update matrix based on a sufficient condition to obtain mutually conjugate search directions. These conditions are shown to be equivalent to the one-parameter Broyden family. Further, we derive a one-to-one correspondence between the Broyden parameter and the scaling between the search directions from the method of conjugate gradients and a quasi-Newton method em- ploying some well-defined update scheme in the one-parameter Broyden family. In paper C, we give necessary and sufficient conditions on the quasi-Newton ma- trix and on the update matrix such that equivalence with the method of conjugate gra- dients hold for the corresponding quasi-Newton method. We show that the set of quasi- Newton schemes admitted by these necessary and sufficient conditions is strictly larger than the one-parameter Broyden family. In addition, we show that this set of quasi- Newton schemes includes an infinite number of symmetric rank-one update schemes. In the second paper (Paper B), we utilize an unnormalized Krylov subspace frame- work for solving symmetric systems of linear equations. These systems may be incom- patible and the matrix may be indefinite/singular. Such systems of symmetric linear equations arise in constrained optimization. In the case of an incompatible symmetric system of linear equations we give a certificate of incompatibility based on a projection on the null space of the symmetric matrix and characterize a minimum-residual solu- tion. Further we derive a minimum-residual method, give explicit recursions for the minimum-residual iterates and characterize a minimum-residual solution of minimum Euclidean norm.
I denna avhandling betraktar vi matematiska egenskaper hos metoder för att lösa symmetriska linjära ekvationssystem som uppkommer i formuleringar och metoder för en mängd olika optimeringsproblem. I första och tredje artikeln (Paper A och Paper C), undersöks kopplingen mellan konjugerade gradientmetoden och kvasi-Newtonmetoder när dessa appliceras på strikt konvexa kvadratiska optimeringsproblem utan bivillkor eller ekvivalent på ett symmet- risk linjärt ekvationssystem med en positivt definit symmetrisk matris. Vi ställer upp villkor på kvasi-Newtonmatrisen och uppdateringsmatrisen så att sökriktningen som fås från motsvarande kvasi-Newtonmetod blir parallell med den sökriktning som fås från konjugerade gradientmetoden. I den första artikeln (Paper A), härleds villkor på uppdateringsmatrisen baserade på ett tillräckligt villkor för att få ömsesidigt konjugerade sökriktningar. Dessa villkor på kvasi-Newtonmetoden visas vara ekvivalenta med att uppdateringsstrategin tillhör Broydens enparameterfamilj. Vi tar också fram en ett-till-ett överensstämmelse mellan Broydenparametern och skalningen mellan sökriktningarna från konjugerade gradient- metoden och en kvasi-Newtonmetod som använder någon väldefinierad uppdaterings- strategi från Broydens enparameterfamilj. I den tredje artikeln (Paper C), ger vi tillräckliga och nödvändiga villkor på en kvasi-Newtonmetod så att nämnda ekvivalens med konjugerade gradientmetoden er- hålls. Mängden kvasi-Newtonstrategier som uppfyller dessa villkor är strikt större än Broydens enparameterfamilj. Vi visar också att denna mängd kvasi-Newtonstrategier innehåller ett oändligt antal uppdateringsstrategier där uppdateringsmatrisen är en sym- metrisk matris av rang ett. I den andra artikeln (Paper B), används ett ramverk för icke-normaliserade Krylov- underrumsmetoder för att lösa symmetriska linjära ekvationssystem. Dessa ekvations- system kan sakna lösning och matrisen kan vara indefinit/singulär. Denna typ av sym- metriska linjära ekvationssystem uppkommer i en mängd formuleringar och metoder för optimeringsproblem med bivillkor. I fallet då det symmetriska linjära ekvations- systemet saknar lösning ger vi ett certifikat för detta baserat på en projektion på noll- rummet för den symmetriska matrisen och karaktäriserar en minimum-residuallösning. Vi härleder även en minimum-residualmetod i detta ramverk samt ger explicita rekur- sionsformler för denna metod. I fallet då det symmetriska linjära ekvationssystemet saknar lösning så karaktäriserar vi en minimum-residuallösning av minsta euklidiska norm.

QC 20150519

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Liao, PaoKuan, and 廖堡寬. "On the Generalized Conjugate Gradient Orthogonal Residual Method." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/51320456719946701524.

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碩士
輔仁大學
數學系研究所
91
In this thesis, we study the generalized conjugate gradient orthogonal residual method (GORES method). It differs from some generalized conjugate gradient methods (GCG methods) on that it uses all the previous search directions at each step, and the method has some advantages over the others. First, it requires storage of only one set of linearly growing number of vectors. Second, at each step, there is only one vector, the residual vector, which must be updated using all the vecors in this set. And third, it is similar to the generalized minimum residual method (GMRES method), but it can stop at any stage when the norm of the residual is sufficiently small and no extra computation is needed to compute this norm. A number of numerical experiments were performed which showed the GORES algorithm performs better than GMRES method in several cases.
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Tiwari, Manasi. "Communication Overlapping Krylov Subspace Methods for Distributed Memory Systems." Thesis, 2022. https://etd.iisc.ac.in/handle/2005/5990.

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Many high performance computing applications in computational fluid dynamics, electromagnetics etc. need to solve a linear system of equations $Ax=b$. For linear systems where $A$ is generally large and sparse, Krylov Subspace methods (KSMs) are used. In this thesis, we propose communication overlapping KSMs. We start with the Conjugate Gradient (CG) method, which is used when $A$ is sparse symmetric positive definite. Recent variants of CG include a Pipelined CG (PIPECG) method which overlaps the allreduce in CG with independent computations i.e., one Preconditioner (PC) and one Sparse Matrix Vector Product (SPMV). As we move towards the exascale era, the time for global synchronization and communication in allreduce increases with the large number of cores available in the exascale systems, and the allreduce time becomes the performance bottleneck which leads to poor scalability of CG. Therefore, it becomes necessary to reduce the number of allreduces in CG and adequately overlap the larger allreduce time with more independent computations than the independent computations provided by PIPECG. Towards this goal, we have developed PIPECG-OATI (PIPECG-One Allreduce per Two Iterations) which reduces the number of allreduces from three per iteration to one per two iterations and overlaps it with two PCs and two SPMVs. For better scalability with more overlapping, we also developed the Pipelined s-step CG method which reduces the number of allreduces to one per s iterations and overlaps it with s PCs and s SPMVs. We compared our methods with state-of-art CG variants on a variety of platforms and demonstrated that our method gives 2.15x - 3x speedup over the existing methods. We have also generalized our research with parallelization of CG on multi-node CPU systems in two dimensions. Firstly, we have developed communication overlapping variants of KSMs other than CG, including Conjugate Residual (CR), Minimum Residual (MINRES) and BiConjugate Gradient Stabilised (BiCGStab) methods for matrices with different properties. The pipelined variants give up to 1.9x, 2.5x and 2x speedup over the state-of-the-art MINRES, CR and BiCGStab methods respectively. Secondly, we developed communication overlapping CG variants for GPU accelerated nodes, where we proposed and implemented three hybrid CPU-GPU execution strategies for the PIPECG method. The first two strategies achieve task parallelism and the last method achieves data parallelism. Our experiments on GPUs showed that our methods give 1.45x - 3x average speedup over existing CPU and GPU-based implementations. The third method gives up to 6.8x speedup for problems that cannot be fit in GPU memory. We also implemented GPU related optimizations for the PIPECG-OATI method and show performance improvements over other GPU implementations of PCG and PIPECG on multiple nodes with multiple GPUs.
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MEZA, JUAN CAMILO. "CONJUGATE RESIDUAL METHODS FOR ALMOST SYMMETRIC LINEAR SYSTEMS." Thesis, 1986. http://hdl.handle.net/1911/15998.

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This study concerns the use of conjugate residual methods for the solution of nonsymmetric linear systems arising from seismic inverse problems. We focus on an application which has two distinguishing features. The first feature is that the linear system is not readily available. The second feature is that the linear system is almost symmetric. We state and prove a new convergence theorem for a class of Generalized Conjugate Residual methods which shows that in some cases the perturbed symmetric problem can be solved with an error bound similar to the one for the symmetric case.
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Book chapters on the topic "Conjugate Residual method"

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Verfürth, R. "A Preconditioned Conjugate Residual Algorithm for the Stokes Problem." In Advances in Multi-Grid Methods, 112–18. Wiesbaden: Vieweg+Teubner Verlag, 1985. http://dx.doi.org/10.1007/978-3-663-14245-4_11.

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Levonyak, Markus, Christina Pacher, and Wilfried N. Gansterer. "Scalable Resilience Against Node Failures for Communication-Hiding Preconditioned Conjugate Gradient and Conjugate Residual Methods." In Proceedings of the 2020 SIAM Conference on Parallel Processing for Scientific Computing, 81–92. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611976137.8.

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Hanke, Martin. "A Minimal Residual Method for Indefinite Problems." In Conjugate Gradient Type Methods for Ill-Posed Problems, 91–126. Routledge, 2017. http://dx.doi.org/10.1201/9781315140193-5.

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Royo, Miriam, and George Barany. "Preparation and handling of peptides containing methionine and cysteine." In Fmoc Solid Phase Peptide Synthesis. Oxford University Press, 1999. http://dx.doi.org/10.1093/oso/9780199637256.003.0008.

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Among the genetically encoded amino acid residues, methionine (Met) and cysteine (Cys) are special because they each contain an atom of sulphur. The present chapter describes how these residues are incorporated into peptides in the context of an Fmoc/tBu solid-phase synthesis strategy, as well as further considerations once the synthetic peptide is released from the support. Of added interest, some manipulations of Cys are advantageously performed at the level of the assembled peptide-resin, prior to cleavage. Many of the aspects discussed here also carry over to the preparation of peptides using a Boc/Bzl strategy. The major problems associated with management of Met reflect the susceptibility of the thioether to alkylation and oxidation. One of the merits of the Fmoc/tBu strategy, in contrast to Boc/Bzl, is that in the former strategy Met is usually introduced without recourse to a protecting group for the thioether side-chain. As documented in this chapter, a proper understanding of acidolytic cleavage conditions and the availability of selective procedures to reverse any inadvertent oxidation are likely to lead to success in obtaining homogeneous peptides containing Met. Management of Cys provides additional significant challenges. For some targets, Cys is required with its side-chain in the free thiol form, whereas for other targets, an even number of Cys residues pair with each other via disulphide linkage(s) to provide cystine residue(s). Disulphide bridges play an important role in the folding and structural stabilization of many natural peptides and proteins, and their artificial introduction into natural or designed peptides is a useful approach to improve biological activities/specificities and stabilities. Furthermore, use of a disulphide bridge is a preferred method to conjugate peptides to protein carriers for increasing the response in immuno-logical studies, to link two separate chains for developing discontinuous epitopes, and to generate active site models. This chapter describes Cys protecting groups, how they are removed to provide either free thiols or disulphides directly, and various strategies and practical considerations to minimize side reactions and maximize formation of the desired products. The thioether side-chain of Met is subject to alkylation and oxidation side reactions, either during the synthetic process or during subsequent handling of the Met-containing peptide.
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Taber, Douglass F. "The Tanino Synthesis of (-)-Glycinoeclepin A." In Organic Synthesis. Oxford University Press, 2013. http://dx.doi.org/10.1093/oso/9780199965724.003.0095.

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(-)-Glycinoeclepin A 3 is effective at pg/mL concentrations as a hatch-stimulating agent for the soybean cyst nematode. Approaching the synthesis of 3, Keiji Tanino of Hokkaido University envisioned (Chemistry Lett. 2010, 39, 835) the convergent coupling of the allylic tosylate 2 with the bridgehead anion 1. The assembly of the fragment 2 was particularly challenging, because the synthesis would require not just the establishment of the two adjacent cyclic quaternary centers but also control of the relative configuration on the sidechain. The preparation of 1 began with the prochiral diketone 3. Enantioselective reduction of the mono enol ether 4 set the absolute configuration of 5. Iodination followed by cyclization then completed the assembly of 1. The construction of the bicyclic tosylate 2 began with m-methyl anisole 7. Following the Rubottom procedure, Birch reduction followed by mild hydrolysis gave the ketone 8. Epoxidation followed by β-elimination delivered the racemic 9, which was exposed to lipase to give, after seven days, the residual alcohol in 40% yield and high ee. The sidechain nitrile was prepared from the diol 12. Homologation gave the nitrile 14, which was equilibrated to the more stable enol ether 15. The two cyclic quaternary centers of 3 were set in a single step by the conjugate addition of the anion of 16 to the crystalline enone 11. Mild hydrolysis of 17 gave the keto aldehyde, which underwent aldol condensation to give the enone 18. The hydroboration of 19 followed by coupling of the intermediate organoborane with 20 delivered 21 with 94:6 relative diastereocontrol. Formylation of the enone 22 followed by triflation and reduction then led to 2. Altough the ketone 1 could be deprotonated with LDA, the only product observed, even at –78°C, was the derived aldol dimer. The metalated dimethylhydrazone 25, in contrast, coupled smoothly with 2 to give, after hydrolyis, the desired adduct 26. Pd-mediated carboxylation of the enol triflate followed by selective oxidative cleavage and hydrolysis then completed the synthesis of (-)-glycinoecleptin A 3.
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Conference papers on the topic "Conjugate Residual method"

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Liao, Hanlin, Hao Deng, and Christian Coddet. "Conjugated Gradient Method for Estimating Inversely the Flux Distribution of Cooling Jets." In ITSC2003, edited by Basil R. Marple and Christian Moreau. ASM International, 2003. http://dx.doi.org/10.31399/asm.cp.itsc2003p0981.

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Abstract It is necessary to cool specimens during spraying in the case APS or HVOF, because process-induced heat rises the specimen temperature and leads to oxidation and spalling of coatings. A reasonable cooling just after spraying improves some properties such as microhardness, adhesion and cohesion of the coating/substrate system. In the modelling of specimen temperature and residual stress, it is necessary to know the flux distribution of the cooling jet like compressed air, CO2 liquid jet etc. Therefore, the evaluation of the flux becomes important. In order to measure and analyse the distribution of cooling flux imposed on the substrate, the theory of the inverse problem of heat conduction was applied and an experimental apparatus was designed to mesure the transient temperature. Because of its insensibility to the effect of measuring error, the conjugate gradient method, an effective method of inverse problems was chosen among several mathematical optimisation methods. The flux distributions of cooling jet can be estimated by using the measured data and a program written according to the conjugate gradient method.
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Blomquist, Matthew, and Abhijit Mukherjee. "Performance Improvements of Krylov Subspace Methods in Numerical Heat Transfer and Fluid Flow Simulations." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-12174.

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Abstract In recent years, advancements in computational hardware have enabled massive parallelism that can significantly reduce the duration of many numerical simulations. However, many high-fidelity simulations use serial algorithms to solve large systems of linear equations and are not well suited to exploit the parallelism of modern hardware. The Tri-Diagonal Matrix Algorithm (TDMA) is one such example of a serial algorithm that is ubiquitous in numerical simulations of heat transfer and fluid flow. Krylov subspace methods for solving linear systems, such as the Bi-Conjugate Gradients (BiCG) algorithm, can offer an ideal solution to improve the performance of numerical simulations as these methods can exploit the massive parallelism of modern hardware. In the present work, Krylov-based linear solvers of Bi-Conjugate Gradients (BCG), Generalized Minimum Residual (GMRES), and Bi-Conjugate Gradients Stabilized (BCGSTAB) have been incorporated into the SIMPLER algorithm to solve a three-dimensional Rayleigh-Bénard Convection model. The incompressible Navier-Stoke’s equations, along with the continuity and energy equations, are solved using the SIMPLER method. The computational duration and numerical accuracy for the Krylov-solvers are compared with that of the TDMA. The results show that Krylov methods can improve the speed of convergence for the SIMPLER method by factors up to 7.7 while maintaining equivalent numerical accuracy to the TDMA.
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Cretu, Spiridon S., Marcelin I. Benchea, and Ovidiu S. Cretu. "Compressive Residual Stresses Effect on Fatigue Life of Rolling Bearings." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43561.

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The fatigue life tests carried out on two groups of ball bearings confirm the positive influence of the compressive residual stresses induced by a previous loading in the elastic-plastic domain. The values of residual stresses are numerically evaluated by employing a three-dimensional strain deformation analysis model. The model is developed in the frame of the incremental theory of plasticity by using the von Mises yield criterion and Prandtl-Reuss equations. To consider the material behaviour the Ramberg-Osgood stress-strain equation is involved and a nonlinear equation is considered to model the influence of the retained austenite. To attain the final load of each loading cycle the two bodies are brought into contact incrementally, so that for each new load increment the new pressure distribution is obtained as the solution of a constrained system of equation. Conjugate gradients method in conjunction with discrete convolution fast Fourier transform is used to solve the huge system of equations. Both the new contact geometry and residual stresses distributions, are further considered as initial values for the next loading cycle, the incremental technique being reiterated. The cyclic evaluation process of both plastic strains and residual stresses is performed until the material shakedowns. Comparisons of the computed residual stresses and deformed profiles with corresponding measured values reveal a good agreement and validate the analysis model. The von Mises equivalent stress, able to include both elastic and residual stresses, is considered in Ioannides-Harris rolling contact fatigue model to obtain theoretical lives of the ball bearings groups. The theoretical analysis reveals also greater fatigue lives for the ball bearings groups with induced residual stresses than the fatigue lives of the group without induced residual stresses.
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Wang, Chenglong, Suizheng Qiu, Wenxi Tian, Yingwei Wu, and Guanghui Su. "Transient Study on Sodium Heat Pipe in Passive Heat Removal System of Molten Salt Reactor." In 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icone21-15029.

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High temperature heat pipes are effective devices for heat transfer, which are characterized by remarkable advantages in conductivity, isothermality and passivity. It is of significance to apply heat pipes on new concept passive residual heat removal system (PRHRS) of molten salt reactor (MSR). In this paper, the transient performance of high temperature sodium heat pipe is simulated with numerical method in the case of MSR accident. The model of the heat pipe is composed of three conjugate heat transfers, i.e. the vapor space, wick structure and wall. Based on finite element method, the governing equations and boundary conditions are solved by using FORTRAN code to acquire the profiles of the temperature, velocity and pressure for the heat pipe transient operation. The results indicated that high temperature sodium heat pipe had a good operating characteristic and removed the residual heat of fuel salt rapidly under the accident of MSR.
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Wallis, J. R., R. P. Kendall, and T. E. Little. "Constrained Residual Acceleration of Conjugate Residual Methods." In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 1985. http://dx.doi.org/10.2118/13536-ms.

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Wang, Zhenfeng, Peigang Yan, Hongyan Huang, and Wanjin Han. "Coupled BEM and FDM Conjugate Analysis of a Three-Dimensional Air-Cooled Turbine Vane." In ASME Turbo Expo 2009: Power for Land, Sea, and Air. ASMEDC, 2009. http://dx.doi.org/10.1115/gt2009-59030.

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A coupled boundary element method (BEM) and finite difference method (FDM) are applied to solve conjugate heat transfer problem of a three-dimensional air-cooled turbine blade. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. In the fluid region, computation code (HIT-NS CODE) adopts the FDM to solve the Navier-Stokes equations. In the solid region, the BEM is adopted to resolve the conduction heat transfer equations. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The solid heat transfer computation code (3D-BEM CODE) is validated by comparing with the results of an analytic solution and the results of commercial code, the results from 3D-BEM CODE have a good agreement with the analytic solution and commercial code results. The BEM uses a weighted residual method to make the Laplace equation convert into a surface integral equation and the surface integral equation is discretized. The BEM avoids the complicated mesh needed in other computation methods and saves the computation time. In addition, the BEM has the characteristic of a combination of an analytic and a discrete solution. So the BEM solutions of heat conduction problems are more accurate. The results of the coupling computation code (HIT-NS-3DBEM CODE) have a good agreement with the experimental results. The adiabatic condition result is different from the results of experiment and code calculation. So the results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines. Four turbulence models are applied: K-epsilon model, K-omega model, K-omega (SST-Gamma Theta) model, and B-L model adopted by computation code. Different turbulence models gives different the results of vane wall temperature. Comparing the four turbulence models, the different turbulence models can exactly simulate the flow field, but they can not give exact values for the heat conduction simulation in the boundary layer. The result of K-Omega (SST-Gamma Theta) turbulence model is closer to the experimental data.
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Abboudi, S., E. A. Artioukhine, and H. Riad. "Estimation of Transient Boundary Conditions in a Multimaterial: Computational and Experimental Analysis." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0735.

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Abstract The goal of the proposed study is to analyze numerically and experimentally transient flux densities absorbed by specimen which is a typical thermal barrier. The studied composite material is obtained by thermal projection of a deposit of MCrAlY on a substrate in Copper. To solve this inverse heat conduction problem, we have used the implicit finite difference method for the direct problem and the iterative regularization method for the inverse problem. The developed numerical algorithm is based on the minimization of the residual functional which is the integrated difference between temperature histories measured and those calculated by solving the direct problem. The conjugate gradient method is used to solve the inverse problem. The residual functional gradient is computed by solving the adjoint problem and the optimal descent parameter is calculated by solving the problem for temperature variations. The heat flux evolution is approximated by cubic B-splines. The method is first validated with simulated numerically data and second validated experimentally by thermal cycling device. Temperature evolutions measured inside the specimen are used to solve the inverse problem.
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8

Kumar, Ravi Ranjan, J. M. McDonough, M. P. Mengu¨c¸, and Illayathambi Kunadian. "Performance Comparison of Numerical Procedures for Efficiently Solving a Microscale Heat Transport Equation During Femtosecond Laser Heating of Nanoscale Metal Films." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79542.

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An alternative discretization and solution procedure for implicitly solving a 3-D microscale heat transport equation during femtosecond laser heating of nanoscale metal films has been developed (Kunadian et al. [1]). The proposed numerical technique directly solves a single partial differential equation, unlike other techniques available in the literature which splits the equation into a system of two equations and then apply discretization. The present paper investigates performance of its split and unsplit methods of solution via numerical experiments using Gauss–Seidel, conjugate gradient, generalized minimal residual and δ-form Douglas–Gunn time-splitting methods to compare the computational cost involved in these methods. The comparison suggests that the unsplit method [1] employing δ-form Douglas–Gunn spatial time-splitting is the most efficient way in terms of CPU time taken to complete the simulation of solving the 3-D time dependent microscale heat transport equation.
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9

Kumar, Rajeev, and Brian H. Dennis. "The Least-Squares Galerkin Split Finite Element Method for Buoyancy-Driven Flow." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29157.

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The least-squares finite element method (LSFEM), based on minimizing the l2-norm of the residual is now well established as a proper approach to deal with the convection dominated fluid dynamic equations. The least-squares finite element method has a number of attractive characteristics such as the lack of an inf-sup condition and the resulting symmetric positive system of algebraic equations unlike Galerkin finite element method (GFEM). However, the higher continuity requirements for second-order terms in the governing equations force the introduction of additional unknowns through the use of an equivalent first-order system of equations or the use of C1 continuous basis functions. These additional unknowns lead to increased memory and computational requirements that have limited the application of LSFEM to large-scale practical problems. A novel finite element method is proposed that employs a least-squares method for first-order derivatives and a Galerkin method for second order derivatives, thereby avoiding the need for additional unknowns required by a pure LSFEM approach. When the unsteady form of the governing equations is used, a streamline upwinding term is introduced naturally by the least-squares method. Resulting system matrix is always symmetric and positive definite and can be solved by iterative solvers like pre-conditioned conjugate gradient method. The method is stable for convection-dominated flows and allows for equal-order basis functions for both pressure and velocity. The method has been successfully applied here to solve complex buoyancy-driven flow with Boussinesq approximation in a square cavity with differentially heated vertical walls using low-order C0 continuous elements.
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10

Kumar, Rajeev, and Brian H. Dennis. "A Least-Squares/Galerkin Finite Element Method for Incompressible Navier-Stokes Equations." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49654.

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Abstract:
The least-squares finite element method (LSFEM), which is based on minimizing the l2-norm of the residual, has many attractive advantages over Galerkin finite element method (GFEM). It is now well established as a proper approach to deal with the convection dominated fluid dynamic equations. The least-squares finite element method has a number of attractive characteristics such as the lack of an inf-sup condition and the resulting symmetric positive system of algebraic equations unlike GFEM. However, the higher continuity requirements for second-order terms in the governing equations force the introduction of additional unknowns through the use of an equivalent first-order system of equations or the use of C1 continuous basis functions. These additional unknowns lead to increased memory and computing time requirements that have prevented the application of LSFEM to large-scale practical problems, such as three-dimensional compressible viscous flows. A simple finite element method is proposed that employs a least-squares method for first-order derivatives and a Galerkin method for second order derivatives, thereby avoiding the need for additional unknowns required by pure a LSFEM approach. When the unsteady form of the governing equations is used, a streamline upwinding term is introduced naturally by the leastsquares method. Resulting system matrix is always symmetric and positive definite and can be solved by iterative solvers like pre-conditioned conjugate gradient method. The method is stable for convection-dominated flows and allows for equalorder basis functions for both pressure and velocity. The stability and accuracy of the method are demonstrated with preliminary results of several benchmark problems solved using low-order C0 continuous elements.
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