Relevant bibliographies by topics / Multigrid methods (Numerical analysis)

Academic literature on the topic 'Multigrid methods (Numerical analysis)'

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Published: 4 June 2021
Last updated: 26 July 2024

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Journal articles on the topic "Multigrid methods (Numerical analysis)"

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Rüde, Ulrich. "Fully Adaptive Multigrid Methods." SIAM Journal on Numerical Analysis 30, no. 1 (February 1993): 230–48. http://dx.doi.org/10.1137/0730011.

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Xu, Jinchao, and Ludmil Zikatanov. "Algebraic multigrid methods." Acta Numerica 26 (May 1, 2017): 591–721. http://dx.doi.org/10.1017/s0962492917000083.

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This paper provides an overview of AMG methods for solving large-scale systems of equations, such as those from discretizations of partial differential equations. AMG is often understood as the acronym of ‘algebraic multigrid’, but it can also be understood as ‘abstract multigrid’. Indeed, we demonstrate in this paper how and why an algebraic multigrid method can be better understood at a more abstract level. In the literature, there are many different algebraic multigrid methods that have been developed from different perspectives. In this paper we try to develop a unified framework and theory that can be used to derive and analyse different algebraic multigrid methods in a coherent manner. Given a smoother$R$for a matrix$A$, such as Gauss–Seidel or Jacobi, we prove that the optimal coarse space of dimension$n_{c}$is the span of the eigenvectors corresponding to the first$n_{c}$eigenvectors$\bar{R}A$(with$\bar{R}=R+R^{T}-R^{T}AR$). We also prove that this optimal coarse space can be obtained via a constrained trace-minimization problem for a matrix associated with$\bar{R}A$, and demonstrate that coarse spaces of most existing AMG methods can be viewed as approximate solutions of this trace-minimization problem. Furthermore, we provide a general approach to the construction of quasi-optimal coarse spaces, and we prove that under appropriate assumptions the resulting two-level AMG method for the underlying linear system converges uniformly with respect to the size of the problem, the coefficient variation and the anisotropy. Our theory applies to most existing multigrid methods, including the standard geometric multigrid method, classical AMG, energy-minimization AMG, unsmoothed and smoothed aggregation AMG and spectral AMGe.
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Kamowitz, David, and Seymour V. Parter. "On MGR$[\nu ]$ Multigrid Methods." SIAM Journal on Numerical Analysis 24, no. 2 (April 1987): 366–81. http://dx.doi.org/10.1137/0724028.

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Braess, D., and R. Verfürth. "Multigrid Methods for Nonconforming Finite Element Methods." SIAM Journal on Numerical Analysis 27, no. 4 (August 1990): 979–86. http://dx.doi.org/10.1137/0727056.

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Apel, Thomas, and Joachim Schöberl. "Multigrid Methods for Anisotropic Edge Refinement." SIAM Journal on Numerical Analysis 40, no. 5 (January 2002): 1993–2006. http://dx.doi.org/10.1137/s0036142900375414.

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Brenner, Susanne C. "Overcoming Corner Singularities Using Multigrid Methods." SIAM Journal on Numerical Analysis 35, no. 5 (October 1998): 1883–92. http://dx.doi.org/10.1137/s0036142996308022.

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Brenner, Susanne C., and Li-yeng Sung. "Multigrid Algorithms for C0 Interior Penalty Methods." SIAM Journal on Numerical Analysis 44, no. 1 (January 2006): 199–223. http://dx.doi.org/10.1137/040611835.

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Wan, Feifei, Yong Yin, Qin Zhang, and Xiuquan Peng. "Analysis of parallel multigrid methods in real-time fluid simulation." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 04 (December 2017): 1750042. http://dx.doi.org/10.1142/s1793962317500428.

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The multigrid method has been widely used in computational fluid dynamics (CFD) numerical calculations because of its strong convergence. To achieve real-time simulation of a fluid in computer graphics (CG), the operation efficiency is also a significant factor to consider except for operational accuracy. For this problem, we introduced two multigrid cycling schemes, V-Cycle and full multigrid (FMG). Moreover, we have proposed a simple geometric multigrid method (GMG), and compared with the existing wide application of algebraic multigrid (AMG). All the calculations are the solution of parallel computing of GPU in this paper. The results showed that our approaches have improved the algorithm’s computational speed and convergence time, which prominently enhanced the efficiency of the fluid simulation.
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Goldstein, Charles I. "Multigrid Methods for Elliptic Problems in Unbounded Domains." SIAM Journal on Numerical Analysis 30, no. 1 (February 1993): 159–83. http://dx.doi.org/10.1137/0730008.

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Boal, Natalia, Francisco Jos´e Gaspar, Francisco Lisbona, and Petr Vabishchevich. "FINITE-DIFFERENCE ANALYSIS FOR THE LINEAR THERMOPOROELASTICITY PROBLEM AND ITS NUMERICAL RESOLUTION BY MULTIGRID METHODS." Mathematical Modelling and Analysis 17, no. 2 (April 1, 2012): 227–44. http://dx.doi.org/10.3846/13926292.2012.662177.

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This paper deals with the numerical solution of a two-dimensional thermoporoelasticity problem using a finite-difference scheme. Two issues are discussed: stability and convergence in discrete energy norms of the finite-difference scheme are proved, and secondly, a distributive smoother is examined in order to find a robust and efficient multigrid solver for the corresponding system of equations. Numerical experiments confirm the convergence properties of the proposed scheme, as well as fast multigrid convergence.
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Dissertations / Theses on the topic "Multigrid methods (Numerical analysis)"

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Au, Wing-hoi. "Numerical generation of body-fitted coordinates by multigrid method /." [Hong Kong] : University of Hong Kong, 1990. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1296637X.

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區榮海 and Wing-hoi Au. "Numerical generation of body-fitted coordinates by multigrid method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B31209555.

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吳朝安 and Chiu-on Ng. "Simulation of initial stage of water impact on 2-D members with multigridded volume of fluid method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B31209361.

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Ng, Chiu-on. "Simulation of initial stage of water impact on 2-D members with multigridded volume of fluid method /." Hong Kong : University of Hong Kong, 1990. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12758073.

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Larson, Gregory J. "Performance of algebraic multigrid for parallelized finite element DNS/LES solvers /." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1559.pdf.

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Eaton, Frank Joseph. "A multigrid preconditioner for two-phase flow in porous media." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3036595.

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Peacock, Darren. "Parallelized multigrid applied to modeling molecular electronics." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101160.

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This thesis begins with a review on the topic of molecular electronics. The purpose of this review is to motivate the need for good theory to understand and predict molecular electronics behaviour. At present the most promising theoretical formalism for dealing with this problem is a combination of density functional theory and nonequilibrium Green's functions (NEGF-DFT). This formalism is especially attractive because it is an ab-initio technique, meaning that it is completely from first principles and does not require any empirical parameters. An implementation of this formalism has been developed by the research group of Hong Guo and is presented and explained here. A few other implementations which are similar but differ in some ways are also discussed briefly to highlight their various advantages and disadvantages.
One of the difficulties of ab-initio calculations is that they can be extremely costly in terms of the computing time and memory that they require. For this reason, in addition to using appropriate approximations, sophisticated numerical analysis tech niques need to be used. One of the bottlenecks in the NEGF-DFT method is solving the Poisson equation on a large real space grid. For studying systems incorporating a gate voltage it is required to be able to solve this problem with nonperiodic boundary conditions. In order to do this a technique called multigrid is used. This thesis examines the multigrid technique and develops an efficient implementation for the purpose of use in the NEGF-DFT formalism. For large systems, where it is necessary to use especially large real space grids, it is desirable to run simulations on parallel computing clusters to handle the memory requirements and make the code run faster. For this reason a parallel implementation of multigrid is developed and tested for performance. The multigrid tool is incorporated into the NEGF-DFT formalism and tested to ensure that it is properly implemented. A few calculations are made on a benzenedithiol system with gold leads to show the effect of an applied gate voltage.
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Chen, Yujia. "Geometric multigrid and closest point methods for surfaces and general domains." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:56a3bf12-ff09-4ea5-b406-9d77054770e2.

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This thesis concerns the analytical and practical aspects of applying the Closest Point Method to solve elliptic partial differential equations (PDEs) on smooth surfaces and domains with smooth boundaries. A new numerical scheme is proposed to solve surface elliptic PDEs and a novel geometric multigrid solver is constructed to solve the resulting linear system. The method is also applied to coupled bulk-surface problems. A new embedding equation in a narrow band surrounding the surface is formulated so that it agrees with the original surface PDE on the surface and has a unique solution which is constant along the normals to the surface. The embedding equation is then discretized using standard finite difference scheme and barycentric Lagrange interpolation. The resulting scheme has 2nd-order accuracy in practice and is provably 2nd-order convergent for curves without boundary embedded in ℝ2. To apply the method to solve elliptic equations on surfaces and domains with boundaries, the "ghost" point approach is adopted to handle Dirichlet, Neumann and Robin boundary conditions. A systematic method is proposed to represent values of ghost points by values of interior points according to boundary conditions. A novel geometric multigrid method based on the closest point representation of the surface is constructed to solve the resulting large sparse linear systems. Multigrid solvers are designed for surfaces with or without boundaries and domains with smooth boundaries. Numerical results indicate that the convergence rate of the multigrid solver stays roughly the same as we refine the mesh, as is desired of a multigrid algorithm. Finally the above methods are combined to solve coupled bulk-surface PDEs with some applications to biology.
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Carter, Paul M. "A multigrid method for determining the deflection of lithospheric plates." Thesis, University of British Columbia, 1988. http://hdl.handle.net/2429/27854.

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Various models are currently in existence for determining the deflection of lithospheric plates under an applied transverse load. The most popular models treat lithospheric plates as thin elastic or thin viscoelastic plates. The equations governing the deflection of such plates have been solved successfully in two dimensions using integral transform techniques. Three dimensional models have been solved using Fourier Series expansions assuming a sinusoidal variation for the load and deflection. In the engineering context, the finite element technique has also been employed. The current aim, however, is to develop an efficient solver for the three dimensional elastic and viscoelastic problems using finite difference techniques. A variety of loading functions may therefore be considered with minimum work involved in obtaining a solution for different forcing functions once the main program has been developed. The proposed method would therefore provide a valuable technique for assessing new models for the loading of lithospheric plates as well as a useful educational tool for use in geophysics laboratories. The multigrid method, which has proved to be a fast, efficient solver for elliptic partial differential equations, is examined as the basis for a solver of both the elastic and viscoelastic problems. The viscoelastic problem, being explicitly time-dependent, is the more challenging of the two and will receive particular attention. Multigrid proves to be a very effective method applicable to the solution of both the elastic and viscoelastic problems.
Science, Faculty of
Mathematics, Department of
Graduate
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Iwamura, Chihiro, and chihiro_iwamura@ybb ne jp. "A fast solver for large systems of linear equations for finite element analysis on unstructured meshes." Swinburne University of Technology, 2004. http://adt.lib.swin.edu.au./public/adt-VSWT20051020.091538.

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The objective of this thesis is to develop a more efficient solver for a large system of linear equations arising from finite element discretization on unstructured tetrahedral meshes for a scalar elliptic partial differential equation of second order for pressure in a commercial computational fluid dynamics (CFD) simulation. Segregated solution methods (or pressure correction type methods) are a widely used approach to obtain solutions of Navier-Stokes equations during numerical simulation by many commercial CFD codes. At each time step, these simulations usually require the approximate solution of a series of scalar equations for velocity, pressure and temperature. Even if the simulation does not require high-accuracy approximations, the large systems of linear equations for pressure may not be efficiently solved. The matrices of these systems of linear equations of real-life industry problems often strongly violate weak diagonal dominance and the numerical simulation often requires solutions of very large systems with over a few hundred thousands degrees of freedom. These conditions produce very ill-conditioned systems of linear equations. Therefore, it is very difficult to solve such systems of linear equations efficiently using most currently available common iterative solvers. A survey of solvers for systems of linear equations was undertaken to determine the preferred solution methodology. An algebraic multigrid preconditioned conjugate gradient (AMGPCG) method solver was chosen for these problems. This solver uses the algebraic multigrid (AMG) cycle as a preconditioner for the conjugate gradient (CG) method. The disadvantages of the conventional AMG method are an expensive setup time and large memory requirements, particularly for three dimensional problems. The disadvantage of an expensive setup time needs to be overcome because the simulation usually requires only low-accuracy approximations for pressure. Also it is important to overcome the disadvantage of the large memory requirements for use in commercial software. In this work, an efficient AMGPCG solver is developed by overcoming the disadvantages of the conventional AMG method. The robustness of AMGPCG is shown theoretically so that the solver is always convergent. Optimum or close to optimum rates of convergence behavior for the solver are shown numerically so that the number of necessary iterations to obtain the estimated solution is approximately independent of mesh resolution. Furthermore, numerical experiments of solving pressure for some industry problems were carried out and compared with other efficient solvers including a fast commercial AMGPCG solver (SAMG, release 20b1). It was found that the developed AMGPCG solver was the fastest among these solvers for solving these problems and its algorithm has been numerically proven to be efficient. In addition, the memory requirement is at an acceptable level for commercial CFD codes.
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Books on the topic "Multigrid methods (Numerical analysis)"

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Multigrid methods. Harlow, Essex, England: Longman Scientific & Technical, 1993.

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1944-, McCormick S. F., ed. Multigrid methods. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1987.

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1948-, Hackbusch W., Trottenberg U, and European Multigrid Conference (3rd : 1990 : Bonn, Germany), eds. Multigrid methods III. Basel: Birkhäuser Verlag, 1991.

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Wesseling, Pieter. An introduction to multigrid methods. Chichester: Wiley, 1992.

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Hung, Chang, and Langley Research Center, eds. On waveform multigrid method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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1950-, Joppich W., ed. Practical Fourier analysis for multigrid methods. Boca Raton, FL: Chapman & Hall/CRC, 2005.

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Briggs, William L. A multigrid tutorial. 2nd ed. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2000.

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Briggs, William L. A multigrid tutorial. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1987.

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Molenaar, J. Multigrid methods for semiconductor device simulation. Amsterdam, the Netherlands: Centrum voor Wiskunde en Informatica, 1993.

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Joppich, Wolfgang. Multigrid Methods for Process Simulation. Vienna: Springer Vienna, 1993.

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Book chapters on the topic "Multigrid methods (Numerical analysis)"

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Hofreither, Clemens, and Walter Zulehner. "Spectral Analysis of Geometric Multigrid Methods for Isogeometric Analysis." In Numerical Methods and Applications, 123–29. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15585-2_14.

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Shah, T. M., D. F. Mayers, and J. S. Rollett. "Analysis and Application of A Line Solver for the Recirculating Flows Using Multigrid Methods." In Numerical Treatment of the Navier-Stokes Equations, 134–44. Wiesbaden: Vieweg+Teubner Verlag, 1990. http://dx.doi.org/10.1007/978-3-663-14004-7_13.

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Panda, Satyananda, and Aleksander Grm. "Multigrid Methods for the Simulations of Surfactant Spreading on a Thin Liquid Film." In Mathematical Modelling, Optimization, Analytic and Numerical Solutions, 287–300. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-0928-5_13.

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Mulder, Wim A. "Numerical Methods, Multigrid." In Encyclopedia of Solid Earth Geophysics, 1–6. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-10475-7_153-1.

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Mulder, Wim A. "Numerical Methods, Multigrid." In Encyclopedia of Solid Earth Geophysics, 895–900. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-90-481-8702-7_153.

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Mulder, Wim A. "Numerical Methods, Multigrid." In Encyclopedia of Solid Earth Geophysics, 1149–54. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-58631-7_153.

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Shapira, Yair. "Multigrid Algorithms." In Numerical Methods and Algorithms, 61–67. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4757-3726-4_4.

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Shapira, Yair. "The Black-Box Multigrid Method." In Numerical Methods and Algorithms, 91–97. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4757-3726-4_7.

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Ginzbourg, I., and G. Wittum. "Multigrid Methods for Two Phase Flows." In Numerical Flow Simulation I, 144–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-540-44437-4_7.

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Wesseling, P. "A survey of Fourier smoothing analysis results." In Multigrid Methods III, 105–27. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-5712-3_7.

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Conference papers on the topic "Multigrid methods (Numerical analysis)"

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Tielen, Roel, Matthias Möller, and Kees Vuik. "Multigrid Reduced in Time for Isogeometric Analysis." In VI ECCOMAS Young Investigators Conference. València: Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12219.

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Isogeometric Analysis [1] has become increasingly popular as an alternative to the Finite Element Method. Solving the resulting linear systems when adopting higher order B-spline basis functions remains a challenging task, as most (standard) iterative methods have a deteriorating preformance for higher values of the approximation order p.Recently, we succesfully applied p-multigrid methods to discretizations arising in IsogeometricAnalysis [2]. In contrast to h-multigrid methods, where each level of the multigrid hierarchycorresponds to a different mesh width h, the p-multigrid hierarchy is constructed based on different approximation orders. The residual equation is then solved at level p = 1, enabling the use of efficient solution techniques developed for low-order standard FEM. Numerical results show that the number of iterations needed for convergence is independent of both h and p when the p-multigrid method is enhanced with a smoother based on an Incomplete LU factorization with dual treshold (ILUT). However, a slight dependence on the number of patches has been observed for multipatch geometries.Since the resulting system matrix has a block structure in case of a multipatch geometry, weconsider the use of block ILUT as a smoother. Results indicate that the use of block ILUT can be an efficient alternative to ILUT on multipatch geometries within a heterogeneous HPC framework. Prelimenary results for p-multigrid methods adopting a block ILUT smoother will be presented in this talk. Furthermore, we investigate the use of alternative multigrid hierarchies, in particular when considering time-dependent problems.REFERENCES[1] T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric Analysis: CAD, Finite Elements,NURBS, Exact Geometry and Mesh Refinement, Computer Methods in Applied Mechanicsand Engineering, 194, 4135 - 4195, 2005[2] R.Tielen, M. Möller, D. Göddeke and C. Vuik, p-multigrid methods and their comparison toh-multigrid methods within Isogeometric Analysis, Computer Methods in Applied Mechanicsand Engineering, 372, 2020
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Luo, P., C. Rodrigo, F. J. Gaspar, and C. W. Oosterlee. "On a multigrid method for the coupled Stokes and porous media flow problem." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992706.

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de Lemos, Marcelo J. S., and Maximilian S. Mesquita. "Multigrid Numerical Solutions of Non-Isothermal Laminar Recirculating Flows." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-1089.

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Abstract The present work investigates the efficiency of the multigrid numerical method applied to solve two-dimensional laminar velocity and temperature fields inside a rectangular domain. Numerical analysis is based on the finite volume discretization scheme applied to structured orthogonal regular meshes. Performance of the correction storage (CS) multigrid algorithm is compared for different inlet Reynolds number (Rein) and number of grids. Up to four grids were used for both V- and W-cycles. Simultaneous and uncoupled temperature-velocity solution schemes were also applied. Advantages in using more than one grid is discussed. Results further indicate an increase in the computational effort for higher Rein and an optimal number of relaxation sweeps for both V- and W-cycles.
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Meng, Xianghui, and Youbai Xie. "Numerical Study of Piston Skirt-Liner Elastohydrodynamic Lubrication and Contact by the Multigrid Method." In ASME 2010 Internal Combustion Engine Division Fall Technical Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/icef2010-35097.

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The cylinder liner-piston system of internal combustion engines is one of the key friction pairs running at the most rigor working conditions. Under the influence of elastohydrodynamic lubrication and contact between the piston skirt and the liner, the dynamic process of piston is a nonlinear and stiff problem difficult to be analyzed accurately and easily. To reach a stable and rapid convergence in analysis, the MEBDF method and the multigrid method are used to solve the piston-skirt elastohydrodynamic lubrication and contact problem. Firstly the solving process of the piston dynamics is analyzed based on the MEBDF method. Then the residual equations for the elastohydrodynamic lubrication pressure are built based on the multigrid method. And the solving method of the nonlinear residual equations is presented based on the quasi Newton-Raphson method. Finally the numerical simulation program is developed based on the MEBDF method and the multigrid method. The elastohydrodynamic lubrication and contact problem of the piston skirt-liner system is simply analyzed based on the simulation. The study in this paper can provide an effective method for tribological analysis and optimization of piston–liner system in the future.
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Xu, Kefan, Guanghui Zhang, Wenlong Sun, and Jiazhen Han. "Static Characteristics Analysis of Textured Thrust Bearing Based on the Multigrid Algorithm." In ASME Turbo Expo 2023: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/gt2023-101497.

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Abstract Carefully designed compliant foil structure or surface texturing can both help improve bearings’ performance. However, little research has been done on their combination: textured gas foil bearing. This paper adopted the modified compressible Reynolds equation as the pressure governing equation of bump-type foil thrust bearing, and the influence of different slip models was discussed. The predicted load capacity agrees with the literature data. This paper further presented the execution time differences between various numerical methods, including the direct, iterative, and multigrid algorithms, when handling the significant discretization effort introduced by texture. The results indicate that the multigrid algorithm performs best, and the execution time is generally reduced by 50% compared to the traditional direct method under the same operating parameters. Besides, further analysis of the textures’ effect on bearings’ performance was carried out based on three distribution types. The results indicate that textures affect all static characteristic parameters more when the relative texture depth increases. For the #1 texture distribution type, the maximum increment of load capacity could exceed 10% when the textures are assumed to be manufactured in the ramp of the top foil. In conclusion, the multigrid is an excellent solution that can balance computational accuracy and efficiency for textured foil thrust bearings. Furthermore, an appropriate arrangement of textures could improve foil thrust bearings’ performance.
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Joppich, W. "A multigrid method for solving the nonlinear diffusion equation on a time-dependent domain using rectangular grids in cartesian coordinates." In [1987] NASECODE V: Fifth International Conference on the Numerical Analysis of Semiconductor Devices and Integrated Circuits. IEEE, 1987. http://dx.doi.org/10.1109/nascod.1987.721187.

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De Palma, P. "Numerical Analysis of Turbomachinery Flows With Transitional Boundary Layers." In ASME Turbo Expo 2002: Power for Land, Sea, and Air. ASMEDC, 2002. http://dx.doi.org/10.1115/gt2002-30223.

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This paper provides a numerical study of the flow through two turbomachinery cascades with transitional boundary layers. The aim of the present work is to validate some state-of-the-art turbulence and transition models in complex flow configurations. Therefore, the compressible Reynolds-averaged Navier–Stokes equations, with an Explicit Algebraic Stress Model (EASM) and k − ω turbulence closure, are considered. Such a turbulence model is combined with the transition model of Mayle for separated flow. The space discretization is based on a finite volume method with Roe’s approximate Riemann solver and formally second-order-accurate MUSCL extrapolation with minmod limiter. Time integration is performed employing an explicit Runge–Kutta scheme with multigrid acceleration. Firstly, the computations of the two- and three-dimensional subsonic flow through the T106 low-pressure turbine cascade are briefly discussed. Then, a more severe test case, involving shock-induced boundary-layer separation and corner stall is considered, namely, the three-dimensional transonic flow through a linear compressor cascade. In the present paper, calculations of such a transonic flow are presented, employing the standard k − ω model and the EASM, without transition model, and a comparison with the experimental data available in the literature is provided.
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Ebna Hai, Bhuiyan Shameem Mahmood, and Markus Bause. "Adaptive Multigrid Methods for Extended Fluid-Structure Interaction (eXFSI) Problem: Part I — Mathematical Modelling." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-53265.

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This contribution is the first part of three papers on Adaptive Multigrid Methods for eXtended Fluid-Structure Interaction (eXFSI) Problem, where we introduce a monolithic variational formulation and solution techniques. In a monolithic nonlinear fluid-structure interaction (FSI), the fluid and structure models are formulated in different coordinate systems. This makes the FSI setup of a common variational description difficult and challenging. This article presents the state-of-the-art of recent developments in the finite element approximation of FSI problem based on monolithic variational formulation in the well-established arbitrary Lagrangian Eulerian (ALE) framework. This research will focus on the newly developed mathematical model of a new FSI problem which is called eXtended Fluid-Structure Interaction (eXFSI) problem in ALE framework. This model is used to design an on-live Structural Health Monitoring (SHM) system in order to determine the wave propagation in moving domains and optimum locations for SHM sensors. eXFSI is strongly coupled problem of typical FSI with a wave propagation problem on the fluid-structure interface, where wave propagation problems automatically adopted the boundary conditions from of the typical FSI problem at each time step. The ALE approach provides a simple, but powerful procedure to couple fluid flows with solid deformations by a monolithic solution algorithm. In such a setting, the fluid equations are transformed to a fixed reference configuration via the ALE mapping. The goal of this work is the development of concepts for the efficient numerical solution of eXFSI problem, the analysis of various fluid-mesh motion techniques and comparison of different second-order time-stepping schemes. This work consists of the investigation of different time stepping scheme formulations for a nonlinear FSI problem coupling the acoustic/elastic wave propagation on the fluid-structure interface. Temporal discretization is based on finite differences and is formulated as an one step-θ scheme; from which we can consider the following particular cases: the implicit Euler, Crank-Nicolson, shifted Crank-Nicolson and the Fractional-Step-θ schemes. The nonlinear problem is solved with Newton’s method whereas the spatial discretization is done with a Galerkin finite element scheme. To control computational costs we apply a simplified version of a posteriori error estimation using the dual weighted residual (DWR) method. This method is used for the mesh adaptation during the computation. The implementation is accomplished via the software library package DOpElib and deal.II for the computation of different eXFSI configurations.
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Tonghui, Yu, Chen Chenwen, and Wang Liqin. "Solution of Load Distribution on the Contact Line of Helical Gears With EHL Theory." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0095.

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Abstract On the base of analysis of the effects of each term in Renolds equaiton on the lubrication state of helical gears, the three dimensional elastohydrodynamic lubrication (EHL) problem is discomposed into two dimensional problems to deal with. A special boundary condition for helical gear EHL problem is led in and applying multigrid method (MGM), numerical solutions for the helical gear EHL problem are accomplished along the contact line. Film shapes and pressure ditributions with typical EHL features are obtained at discreted points on the contact line. The procedure presented here to calculate the load distribution on the contact line can also be used to calculate the load shares among different contact lines.
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Fatima, Arooj, Stefan Turek, Abderrahim Ouazzi, and Muhammad Aaqib Afaq. "An adaptive discrete Newton method for regularization-free Bingham model." In VI ECCOMAS Young Investigators Conference. València: Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12389.

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Developing a numerical and algorithmic tool which correctly identifies unyielded region in the yield stress fluid flow is a challenging task. Two approaches are commonly used to handle the singular behaviour at the yield surface, i.e. Augmented Lagrangian approach and the regularization approach, respectively. Generally in the regularization approach, solvers do not perform efficiently when the regularization parameter gets very small. In this work, we use a formulation introducing a new auxiliary stress [1]. The three field formulation of yield stress fluid corresponds to a regularization-free Bingham formulation. The resulting set of equations arising from the three field formulation is solved efficiently and accurately by a monolithic finite element method. The velocity and pressure are discretized by higher order stable FEM pair $Q_2/P^{\text{disc}}_1$ and the auxiliary stress is discretized by $Q_2$ element.Furthermore, this problem is highly nonlinear and presents a big challenge to any nonlinear solver. We developed a new adaptive discrete Newton's method, which evaluates the Jacobian with the directional divided difference approach [2]. The step length in this process is an important key: We relate this length to the rate of the actual nonlinear reduction for achieving a robust adaptive Newton's method. The resulting linear sub problems are solved using the geometrical multigrid solver. We analyse the solvability of the problem along with the adaptive Newton method for Bingham fluids by doing numerical studies for two different prototypical configurations, i.e. "Viscoplastic fluid flow in a channel" and "Lid Driven Cavity", respectively [2].REFERENCES[1] Aposporidis, A., Haber, E., Olshanskii, M. A. and Veneziani, A. A mixed formulation of the Bingham fluid flow problem: Analysis and numerical solution. Comput. Methods Appl. Mech. Engrg, Vol. 200, pp. 2434–2446, (2011).[2] Fatima, A., Turek, S., Ouazzi, A. and Afaq, M. A. An adaptive discrete Newton method for regularization-free Bingham model. Ergebnisberichte des Instituts fuer Angewandte Mathematik Nummer 635, Fakultaet fuer Mathematik, TU Dortmund University, 635, 2021.
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Reports on the topic "Multigrid methods (Numerical analysis)"

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Rozovskii, Boris, and Alexander Tartakovsky. Nonlinear Filtering: Analysis and Numerical Methods. Fort Belvoir, VA: Defense Technical Information Center, November 2001. http://dx.doi.org/10.21236/ada399200.

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Flanagan, R. D., M. A. Tenbus, and R. M. Bennett. Numerical methods for analysis of clay tile infills. Office of Scientific and Technical Information (OSTI), October 1993. http://dx.doi.org/10.2172/10186487.

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Padgett, James. Effectiveness of Additive Correction Multigrid in numerical heat transfer analysis when implemented on an Intel IPSC2. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.6313.

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Clayton, John D., Peter W. Chung, Michael A. Greenfield, and WIlliam D. Nothwang. Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids. Fort Belvoir, VA: Defense Technical Information Center, December 2006. http://dx.doi.org/10.21236/ada459751.

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Page, William, Brian Fisk, and William Zimmerman. Development of Numerical Simulation Methods for Analysis of Laser Guided Arc Discharge. Fort Belvoir, VA: Defense Technical Information Center, February 2008. http://dx.doi.org/10.21236/ada483004.

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Eisenberg, Michael. Descriptive Simulation: Combining Symbolic and Numerical Methods in the Analysis of Chemical Reaction Mechanisms. Fort Belvoir, VA: Defense Technical Information Center, September 1989. http://dx.doi.org/10.21236/ada214678.

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Citerley, Richard L., and Narendra S. Khot. Numerical Methods for Imperfection Sensitivity Analysis of Stiffened Cylindrical Shells. Volume 1. Development and Applications. Fort Belvoir, VA: Defense Technical Information Center, September 1986. http://dx.doi.org/10.21236/ada179686.

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Chan, Tony F. Numerical Methods for Solving Large Sparse Eigenvalue Problems and for the Analysis of Bifurcation Phenomena. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada244273.

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Chan, Tony F. Numerical Methods for Solving Large Sparse Eigenvalue Problems and for the Analysis of Bifurcation Phenomena. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada246470.

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Ihlenburg, Frank, and Ivo Babuska. Dispersion Analysis and Error Estimation of Galerkin Finite Element Methods for the Numerical Computation of Waves. Fort Belvoir, VA: Defense Technical Information Center, July 1994. http://dx.doi.org/10.21236/ada290296.

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