Relevant bibliographies by topics / Iterative Solvers (Preconditioned Conjugate Gradient)

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

Academic literature on the topic 'Iterative Solvers (Preconditioned Conjugate Gradient)'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Iterative Solvers (Preconditioned Conjugate Gradient)"

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Bertolazzi, Enrico, and Marco Frego. "Preconditioning Complex Symmetric Linear Systems." Mathematical Problems in Engineering 2015 (2015): 1–20. http://dx.doi.org/10.1155/2015/548609.

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A new preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to conjugate orthogonal conjugate gradient (COCG) or conjugate orthogonal conjugate residual (COCR) iterative solvers and does not require any estimation of the spectrum of the coefficient matrix. An upper bound of the condition number of the preconditioned linear system is provided. To reduce the computational cost the preconditioner is approximated with an inexact variant based on incomplete Cholesky decomposition or on orthogonal polynomials. Numerical results show that the present preconditioner and its inexact variant are efficient and robust solvers for this class of linear systems. A stability analysis of the inexact polynomial version completes the description of the preconditioner.
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Camargos, Ana Flávia P., Viviane C. Silva, Jean-M. Guichon, and Gérard Meunier. "GPU-accelerated iterative solution of complex-entry systems issued from 3D edge-FEA of electromagnetics in the frequency domain." International Journal of High Performance Computing Applications 31, no. 2 (July 28, 2016): 119–33. http://dx.doi.org/10.1177/1094342015584476.

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We present a performance analysis of a parallel implementation for both preconditioned conjugate gradient and preconditioned bi-conjugate gradient solvers running on graphic processing units (GPUs) with CUDA programming model. The solvers were mainly optimized for the solution of sparse systems of algebraic equations at complex entries, arising from the three-dimensional edge-finite element analysis of the electromagnetic phenomena involved in the open-bound earth diffusion of currents under time-harmonic excitation. We used a shifted incomplete Cholesky (IC) factorization as preconditioner. Results show a significant speedup by using either a single-GPU or a multi-GPU device, compared to a serial central processing unit (CPU) implementation, thereby allowing the simulations of large-scale problems in low-cost personal computers. Additional experiments of the optimized solvers show that its use can be extended successfully to other complex systems of equations arising in electrical engineering, such as those obtained in power–system analysis.
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Jin, Xiao-Qing, Fu-Rong Lin, and Zhi Zhao. "Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations." Communications in Computational Physics 18, no. 2 (July 30, 2015): 469–88. http://dx.doi.org/10.4208/cicp.120314.230115a.

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AbstractIn this paper, preconditioned iterative methods for solving two-dimensional space-fractional diffusion equations are considered. The fractional diffusion equation is discretized by a second-order finite difference scheme, namely, the Crank-Nicolson weighted and shifted Grünwald difference (CN-WSGD) scheme proposed in [W. Tian, H. Zhou and W. Deng, A class of second order difference approximation for solving space fractional diffusion equations, Math. Comp., 84 (2015) 1703-1727]. For the discretized linear systems, we first propose preconditioned iterative methods to solve them. Then we apply the D’Yakonov ADI scheme to split the linear systems and solve the obtained splitting systems by iterative methods. Two preconditioned iterative methods, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient normal residual (preconditioned CGNR) method, are proposed to solve relevant linear systems. By fully exploiting the structure of the coefficient matrix, we design two special kinds of preconditioners, which are easily constructed and are able to accelerate convergence of iterative solvers. Numerical results show the efficiency of our preconditioners.
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Qiu, Changkai, Changchun Yin, Yunhe Liu, Xiuyan Ren, Hui Chen, and Tingjie Yan. "Solution of large-scale 3D controlled-source electromagnetic modeling problem using efficient iterative solvers." GEOPHYSICS 86, no. 4 (June 30, 2021): E283—E296. http://dx.doi.org/10.1190/geo2020-0461.1.

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With geophysical surveys evolving from traditional 2D to 3D models, the large volume of data adds challenges to inversion, especially when aiming to resolve complex 3D structures. An iterative forward solver for the controlled-source electromagnetic (CSEM) method requires less memory than that for a direct solver; however, it is not easy to iteratively solve an ill-conditioned linear system of equations arising from finite-element discretization of Maxwell’s equations. To solve this problem, we have developed efficient and robust iterative solvers for frequency- and time-domain CSEM modeling problems. For the frequency-domain problem, we first transform the linear system into its equivalent real-number format, and then introduce an optimal block-diagonal preconditioner. Because the condition number of the preconditioned linear equation system has an upper bound of [Formula: see text], we can achieve fast solution convergence when applying a flexible generalized minimum residual solver. Applying the block preconditioner further results in solving two smaller linear systems with the same coefficient matrix. For the time-domain problem, we first discretize the partial differential equation for the electric field in time using an unconditionally stable backward Euler scheme. We then solve the resulting linear equation system iteratively at each time step. After the spatial discretization in the frequency domain, or space-time discretization in the time domain, we exploit the conjugate-gradient solver with auxiliary-space preconditioners derived from the Hiptmair-Xu decomposition to solve these real linear systems. Finally, we check the efficiency and effectiveness of our iterative methods by simulating complex CSEM models. The most significant advantage of our approach is that the iterative solvers we adopt have almost the same accuracy and robustness as direct solvers but require much less memory, rendering them more suitable for large-scale 3D CSEM forward modeling and inversion.
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Bello, Musa, Jianxin Liu, and Rongwen Guo. "Three-Dimensional Wide-Band Electromagnetic Forward Modelling Using Potential Technique." Applied Sciences 9, no. 7 (March 29, 2019): 1328. http://dx.doi.org/10.3390/app9071328.

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The efficacy of Krylov subspace solvers is strongly dependent on the preconditioner applied to solve the large sparse linear systems of equation for electromagnetic problems. In this study, we present a three-dimensional (3-D) plane wave electromagnetic forward simulation over a broadband frequency range. The Maxwell’s equation is solved in a secondary formulation of the Lorentz gauge coupled-potential technique. A finite-volume scheme is employed for discretizing the system of equations on a structured rectilinear mesh. We employed a block incomplete lower-upper factorization (ILU) preconditioner that is suitable for our potential formulation to enhance the computing time and convergence of the systems of equation by comparing with other preconditioners. Furthermore, we observe their effect on the iterative solvers such as the quasi-minimum residual and bi-conjugate gradient stabilizer. Several applications were used to validate and test the effectiveness of our method. Our scheme shows good agreement with the analytical solution. Notably, from the marine hydrocarbon and the crustal model, the utilisation of the bi-conjugate gradient stabilizer with block ILU preconditioner is the most appropriate. Thus, our approach can be incorporated to optimize the inversion process.
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Puglisi, Giuseppe, Davide Poletti, Giulio Fabbian, Carlo Baccigalupi, Luca Heltai, and Radek Stompor. "Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets." Astronomy & Astrophysics 618 (October 2018): A62. http://dx.doi.org/10.1051/0004-6361/201832710.

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Context. An estimation of the sky signal from streams of time ordered data (TOD) acquired by the cosmic microwave background (CMB) experiments is one of the most important steps in the context of CMB data analysis referred to as the map-making problem. The continuously growing CMB data sets render the CMB map-making problem progressively more challenging in terms of computational cost and memory in particular in the context of ground-based experiments with their operational limitations as well as the presence of contaminants. Aims. We study a recently proposed, novel class of the Preconditioned Conjugate Gradient (PCG) solvers which invoke two-level preconditioners in the context of the ground-based CMB experiments. We compare them against the PCG solvers commonly used in the map-making context considering their precision and time-to-solution. Methods. We compare these new methods on realistic, simulated data sets reflecting the characteristics of current and forthcoming CMB ground-based experiments. We develop a divide-and-conquer implementation of the approach where each processor performs a sequential map-making for a subset of the TOD. Results. We find that considering the map level residuals, the new class of solvers permits us to achieve a tolerance that is better than the standard approach by up to three orders of magnitude, where the residual level often saturates before convergence is reached. This often corresponds to an important improvement in the precision of the recovered power spectra in particular on the largest angular scales. The new method also typically requires fewer iterations to reach a required precision and therefore shorter run times are required for a single map-making solution. However, the construction of an appropriate two-level preconditioner can be as costly as a single standard map-making run. Nevertheless, if the same problem needs to be solved multiple times, for example, as in Monte Carlo simulations, this cost is incurred only once, and the method should be competitive, not only as far as its precision is concerned but also its performance.
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Ju, S. H., and H. H. Hsu. "An Out-of-Core Eigen-Solver with OpenMP Parallel Scheme for Large Spare Damped System." International Journal of Computational Methods 16, no. 07 (July 26, 2019): 1950038. http://dx.doi.org/10.1142/s0219876219500385.

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An out-of-core block Lanczos method with the OpenMP parallel scheme was developed to solve large spare damped eigenproblems. The symmetric generalized eigenproblem is first solved using the block Lanczos method with the preconditioned conjugate gradient (PCG) method, and the condensed damped eigenproblem is then solved to obtain the complex eigenvalues. Since the PCG solvers and out-of-core schemes are used, a large-scale eigenproblem can be solved using minimal computer memory. The out-of-core arrays only need to be read once in each Lanczos iteration, so the proposed method requires little extra CPU time. In addition, the second-level OpenMP parallel computation in the PCG solver is suggested to avoid using a large block size that often increases the number of iterations needed to achieve convergence.
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Moutafis, Byron E., George A. Gravvanis, and Christos K. Filelis-Papadopoulos. "Hybrid multi-projection method using sparse approximate inverses on GPU clusters." International Journal of High Performance Computing Applications 34, no. 3 (February 13, 2020): 282–305. http://dx.doi.org/10.1177/1094342020905637.

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The state-of-the-art supercomputing infrastructures are equipped with accelerators, such as graphics processing units (GPUs), that operate as coprocessors for each workstation of the distributed memory system. The multi-projection type methods are a class of algebraic domain decomposition methods based on semi-aggregation techniques. The multi-projection type methods have improved convergence behavior, as the number of subdomains increases, due to the corresponding augmentation of the semi-aggregated local linear systems with more coarse components, while the number of fine components is reduced. Moreover, limited amount of communications among the workstations is required by the proposed method. The utilization of the available GPUs allows an increase in the number of subdomains along with finer-grained parallelism, leading to improved performance. A load-balancing algorithm that ensures the concurrency of the computations on multicore processors and GPUs is proposed. Flexible parallel preconditioned Krylov subspace iterative methods enhanced with multi-projection type methods have been designed appropriately in order to have improved performance, compared to CPU-only or GPU-only executions, by exploiting the available CPUs and GPUs of the distributed memory system concurrently. The unsymmetric local linear systems are solved by the preconditioned Bi-Conjugate Gradient STABilized (BiCGSTAB) method enhanced with the modified generic factored approximate sparse inverse preconditioner, whereas the preconditioned conjugate gradient (CG) method along with the symmetric factored approximate sparse inverse preconditioner is used for the symmetric positive definite local coefficient matrices. Numerical results regarding the convergence behavior, the performance, and the scalability of the proposed method for several problems are given.
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Betté, Srinivas, Julio C. Diaz, William R. Jines, and Trond Steihaug. "A block preconditioned conjugate gradient-type iterative solver for linear systems in thermal reservoir simulation." Journal of Computational Physics 67, no. 1 (November 1986): 37–58. http://dx.doi.org/10.1016/0021-9991(86)90114-2.

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Bergamaschi, Luca. "A Survey of Low-Rank Updates of Preconditioners for Sequences of Symmetric Linear Systems." Algorithms 13, no. 4 (April 21, 2020): 100. http://dx.doi.org/10.3390/a13040100.

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The aim of this survey is to review some recent developments in devising efficient preconditioners for sequences of symmetric positive definite (SPD) linear systems A k x k = b k , k = 1 , … arising in many scientific applications, such as discretization of transient Partial Differential Equations (PDEs), solution of eigenvalue problems, (Inexact) Newton methods applied to nonlinear systems, rational Krylov methods for computing a function of a matrix. In this paper, we will analyze a number of techniques of updating a given initial preconditioner by a low-rank matrix with the aim of improving the clustering of eigenvalues around 1, in order to speed-up the convergence of the Preconditioned Conjugate Gradient (PCG) method. We will also review some techniques to efficiently approximate the linearly independent vectors which constitute the low-rank corrections and whose choice is crucial for the effectiveness of the approach. Numerical results on real-life applications show that the performance of a given iterative solver can be very much enhanced by the use of low-rank updates.
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Dissertations / Theses on the topic "Iterative Solvers (Preconditioned Conjugate Gradient)"

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O'Neal, Jerome W. "The use of preconditioned iterative linear solvers in interior-point methods and related topics." Diss., Available online, Georgia Institute of Technology, 2005, 2005. http://etd.gatech.edu/theses/available/etd-06242005-162854/.

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Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2006.
Parker, R. Gary, Committee Member ; Shapiro, Alexander, Committee Member ; Nemirovski, Arkadi, Committee Member ; Green, William, Committee Member ; Monteiro, Renato, Committee Chair.
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Solov'ëv, Sergey I. "Preconditioned iterative methods for monotone nonlinear eigenvalue problems." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600657.

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This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue problem, we suggest preconditioned iterative methods: preconditioned simple iteration method, preconditioned steepest descent method, and preconditioned conjugate gradient method. These methods use only matrix-vector multiplications, preconditioner-vector multiplications, linear operations with vectors and inner products of vectors. We investigate the convergence and derive grid-independent error estimates of these methods for computing eigenvalues. Numerical experiments demonstrate practical effectiveness of the proposed methods for a class of mechanical problems.
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Bounaim, Aïcha. "Méthodes de décomposition de domaine : application à la résolution de problèmes de contrôle optimal." Phd thesis, Université Joseph Fourier (Grenoble), 1999. http://tel.archives-ouvertes.fr/tel-00004809.

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Ce travail porte sur l'étude des méthodes de décomposition de domaine et leur application pour résoudre des problèmes de contrôle optimal régis par des équations aux dérivées partielles. Le principe de ces méthodes consiste à ramener des problèmes de grande taille sur des géométries complexes en une suite de sous-problèmes de taille plus petite sur des géométries plus simples. En considérant une décomposition sans recouvrement, l'intérêt de ces méthodes pour les problèmes de contrôle optimal réside au niveau de l'intégration de l'équation d'état, puisqu'il est possible de partitionner le problème en une suite de problèmes plus petits, quitte à contraindre les interfaces entre les sous-domaines à obéir à des conditions de raccordement afin de déduire la solution globale à partir des solutions locales. Dans une première partie, nous étudions le cas elliptique. Nous considérons simultanément la minimisation de la fonction coût et des raccordements sur les frontières entre les sous-domaines. Cette combinaison de problèmes de minimisation et de méthodes de décomposition de domaine est traitée par des techniques de Lagrangien augmenté. Nous montrons que, sur le domaine décomposé, le problème initial se réduit à la recherche d'un point-selle. Une étude des méthodes de Lagrangien nous a permis de choisir une variante d'algorithmes existants dans la littérature et de les combiner avec un algorithme de décomposition de domaine. Dans la seconde partie, nous développons l'extension de cette approche aux problèmes de contrôle optimal régis par des systèmes paraboliques en considérant uniquement une décomposition en espace du domaine de calcul. Dans une dernière partie, nous considérons une décomposition de domaine avec recouvrement à chaque pas de la minimisation. D'une part, nous construisons un algorithme parallèle en utilisant la méthode de Schwarz multiplicative en tant que solveur. Ceci permet de déduire naturellement l'état adjoint par transposition des systèmes directs locaux. L'algorithme global défini par la méthode de minimisation de type quasi-Newton et ce solveur de Schwarz constitue une méthode robuste de résolution du problème de contrôle optimal, mais coûteuse. D'autre part, et plus particulièrement, pour des problèmes de grande taille, l'algorithme de type quasi-Newton, combiné avec le solveur de Krylov BiCGSTAB préconditionné par une méthode de Schwarz additive, est plus compétitif dans la mesure oû l'on obtient de bonnes performances parallèles. De nombreux résultats sont présentés pour préciser le comportement des algorithmes d'optimisation quand ils sont utilisés avec des méthodes de Schwarz.
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Rocha, João Miguel Lopes de Almeida. "Aceleração GPU da animação de superfícies deformáveis." Master's thesis, FCT - UNL, 2008. http://hdl.handle.net/10362/1880.

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Dissertação de Mestrado em Engenharia Informática
A simulação de tecidos virtuais desempenha um papel importante em diversas áreas, como as indústrias dos jogos de computador e do cinema, sendo um tópico de investigação com grande actividade. A simulação é, normalmente, efectuada recorrendo a sistemas de partículas. Sobre as partículas são, de uma forma geral, definidas uma série de interacções com base num modelo físico de superfície, que caracteriza as propriedades do tecido, sobretudo no que diz respeito às suas deformações internas. A simulação é uma tarefa de computação extremamente intensiva graças a factores como a avaliação do modelo da superfície ou a utilização de métodos de integração numérica para a resolução do sistema de equações diferenciais que determinam a dinâmica do tecido. Qualquer destes factores depende, de forma directa, do número de partículas usado para discretizar a superfície. Na área da computação gráfica, alguns trabalhos foram já realizados no sentido de acelerar a animação da simulação de tecidos através da programação de GPU, como em [Zel05], [Zel07] e [Den06]. O GPU moderno contém vários processadores especializados em processar grandes quantidades de dados em paralelo, apresentando uma capacidade computacional, no que toca ao número de operações de vírgula flutuante por unidade de tempo, muito superior à do CPU, sendo particularmente apropriado a problemas que possam ser expressos como computações paralelas com alta intensidade de cálculo matemático. Neste trabalho, pretende-se contribuir com a aceleração de um simulador de tecidos com realismo acrescido, desenvolvido em [Birr07], recorrendo a um modelo de hardware e programação para GPU inovador, que o apresenta como um verdadeiro co-processador genérico ao CPU, o NVIDIA CUDA [Cud07]. As contribuições previstas estendem-se à realização de um estudo sobre as vantagens e desvantagens da utilização deste modelo quando comparado com outros, como [Zel05], [Zel07] ou [Den06], através de uma análise cuidada dos resultados obtidos, bem como quais as melhores soluções conseguidas na prática.
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Book chapters on the topic "Iterative Solvers (Preconditioned Conjugate Gradient)"

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Fillmore, Travis B., Varun Gupta, and Carlos Armando Duarte. "Preconditioned Conjugate Gradient Solvers for the Generalized Finite Element Method." In Meshfree Methods for Partial Differential Equations IX, 1–17. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15119-5_1.

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Peng, Jie, Shi Shu, Chunsheng Feng, and Xiaoqiang Yue. "BPX-Like Preconditioned Conjugate Gradient Solvers for Poisson Problem and Their CUDA Implementations." In Advances in Intelligent Systems and Computing, 633–43. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-38789-5_70.

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Conference papers on the topic "Iterative Solvers (Preconditioned Conjugate Gradient)"

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Kushida, Noriyuki, Hiroshi Okuda, and Genki Yagawa. "Large-Scale Parallel Finite Element Analysis of the Stress Singular Problems." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22562.

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In this paper, the convergence behavior of large-scale parallel finite element method for the stress singular problems was investigated. The convergence behavior of iterative solvers depends on the efficiency of the preconditioners. However, efficiency of preconditioners may be influenced by the domain decomposition that is necessary for parallel FEM. In this study the following results were obtained: Conjugate gradient method without preconditioning and the diagonal scaling preconditioned conjugate gradient method were not influenced by the domain decomposition as expected. symmetric successive over relaxation method preconditioned conjugate gradient method converged 6% faster as maximum if the stress singular area was contained in one sub-domain.
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Xuewei Ping and Tie Jun Cui. "The SSOR preconditioned bi-conjugate gradient iterative solver for finite element solution of scattering problems." In 2009 International Conference on Microwave Technology and Computational Electromagnetics (ICMTCE 2009). IET, 2009. http://dx.doi.org/10.1049/cp.2009.1341.

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Mut, Fernando, Romain Aubry, Guillaume Houzeaux, Juan Cebral, and Rainald Lohner. "Deflated Preconditioned Conjugate Gradient Solvers: Extensions and Improvements." In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-118.

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Mut, Fernando, Romain Aubry, Guillaume Pierrot, Jean Roger, Juan Cebral, and Rainald Lohner. "Coarse-Grain Deflation for Preconditioned Conjugate Gradient Solvers: Application to the Pressure Poisson Equation." In 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-165.

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Sowayan, A. S., A. Bénard, and A. R. Diaz. "A Wavelets Method for Solving Heat Transfer and Viscous Fluid Flow Problems." In ASME 2013 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/fedsm2013-16312.

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Wavelet-based methods have demonstrated great potential for solving partial differential equations of various types. The capabilities of the wavelet Galerkin method are explored by solving various heat transfer and fluid flow problems. A fictitious domain approach is used to simplify the discretization of the domain and a penalty method allows an efficient implementation of the boundary conditions. The resulting system of equation is solved iteratively via the Conjugate Gradient and Preconditioned Conjugate Gradient Methods. The fluid flow problems in the present study are formulated in such a manner that the solution of the continuity and momentum equations is obtained by solving a series of Poisson equations. This is achieved by using steepest descent method. The examples solved show that the method is amenable to solving large problems rapidly with modest computational resources.
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Tanaka, Nobuatsu. "Wavelet-Preconditioned Conjugate Gradient Poisson Solver and Its Use in Parallel Processing: Application of Haar Wavelet." In ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/fedsm2002-31119.

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Haar-wavelet-based preconditioning technique for conjugate gradient Poisson solvers is described. The proposed method is suitable for parallel processing because of data locality. The method also has a superior property of preventing the computing time from increasing markedly with the increase in the number of grid points. These kinds of combined approaches of software and hardware are superior in large scale problems and will play more important roles in future computational science.
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Yue, Xiaoqiang, Shi Shu, and Chunsheng Feng. "UA-AMG Methods for 2-D 1-T Radiation Diffusion Equations and Their CPU-GPU Implementations." In 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icone21-16157.

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In this paper, we study several unsmoothed aggregation based algebraic multigrid (UA-AMG) methods with regard to different characteristics of CPUs and graphics processing units (GPUs). We propose some UA-AMG methods with lower computational complexity for CPU and CPU-GPU, and study these UA-AMG methods mixing with 4 kinds of red-black colored Gauss-Seidel smoothers for CPU-GPU since the initial mesh is structured. These UA-AMG methods are used as preconditioners for the conjugate gradient (CG) solver to solve a class of two-dimensional single-temperature radiation diffusion equations discretized by preserving symmetry finite volume element scheme. Numerical results demonstrate that, UA-NA-CG-s, which wins the best robustness and efficiency among them, is much more efficient than the default AMG preconditioned CG solvers in HYPRE, AGMG and Cusp for CPU; Under CPU-GPU, UA-W-CG-p is the most robust and efficient one, and rather more efficient than the smoothed aggregation based AMG preconditioned CG solver in Cusp.
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Kotteda, V. M. Krushnarao, Ashesh Chattopadhyay, Vinod Kumar, and William Spotz. "Next-Generation Multiphase Flow Solver for Fluidized Bed Applications." In ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/fedsm2017-69555.

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A framework is developed to integrate MFiX (Multiphase Flow with Interphase eXchanges) with advanced linear solvers in Trilinos. MFiX is a widely used open source general purpose multiphase solver developed by National Energy Technology Laboratories and written in Fortran. Trilinos is an objected-oriented open source software development platform from Sandia National Laboratories for solving large scale multiphysics problems. The framework handles the different data structures in Fortran and C++ and exchanges the information from MFiX to Trilinos and vice versa. The integrated solver, called MFiX-Trilinos hereafter, provides next-generation computational capabilities including scalable linear solvers for distributed memory massively parallel computers. In this paper, the solution from the standard linear solvers in MFiX-Trilinos is validated against the same from MFiX for 2D and 3D fluidized bed problems. The standard iterative solvers considered in this work are Bi-Conjugate Gradient Stabilized (BiCGStab) and Generalized minimal residual methods (GMRES) as the matrix is non-symmetric in nature. The stopping criterion set for the iterative solvers is same. It is observed that the solution from the integrated solver and MFiX is in good agreement.
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Dennis, Brian H. "The Inverse Least-Squares Finite Element Method Applied to the Convection-Diffusion Equation." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12083.

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A Least Squares Finite Element Method (LSFEM) formulation for the detection of unknown boundary conditions in problems governed by the steady convection-diffusion equation will be presented. The method is capable of determining temperatures, and heat fluxes in location where such quantities are unknown provided such quantities are sufficiently over-specified in other locations. For the current formulation it is assumed the velocity field is known. The current formulation is unique in that it results in a sparse square system of equations even for partial differential equations that are not self-adjoint. Since this formulation always results in a symmetric positive-definite matrix, the solution can be found with standard sparse matrix solvers such as preconditioned conjugate gradient method. In addition, the formulation allows for equal order approximation of temperature and heat fluxes as it is not subject to the inf-sup condition. The formulation allow for a treatment of over-specified boundary conditions. Also, various forms of regularization can be naturally introduced within the formulation. Details of the discretization and sample results will be presented.
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Kumar, Rajeev, and Brian H. Dennis. "A Least-Squares Galerkin Split Finite Element Method for Compressible Navier-Stokes Equations." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87569.

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Abstract:
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 stability and accuracy of the method are demonstrated in the context of compressible flows by results of few compressible benchmark problems solved using low-order C0 continuous elements.
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Reports on the topic "Iterative Solvers (Preconditioned Conjugate Gradient)"

1

Moridis, G., K. Pruess, and E. Antunez. T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2. Office of Scientific and Technical Information (OSTI), March 1994. http://dx.doi.org/10.2172/145291.

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2

Oppe, T., W. Joubert, and D. Kincaid. NSPCG (Nonsymmetric Preconditioned Conjugate Gradient) user's guide: Version 1. 0: A package for solving large sparse linear systems by various iterative methods. Office of Scientific and Technical Information (OSTI), April 1988. http://dx.doi.org/10.2172/7035748.

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