Relevant bibliographies by topics / Multigrid solution strategy

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  1. Journal articles
  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Multigrid solution strategy'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Multigrid solution strategy"

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Rahman, Mohammad Tanvir, and Alfio Borzì. "A FEM-Multigrid Scheme for Elliptic Nash-Equilibrium Multiobjective Optimal Control Problems." Numerical Mathematics: Theory, Methods and Applications 8, no. 2 (May 2015): 253–82. http://dx.doi.org/10.4208/nmtma.2015.w11si.

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AbstractA finite-element multigrid scheme for elliptic Nash-equilibrium multiobjective optimal control problems with control constraints is investigated. The multigrid computational framework implements a nonlinear multigrid strategy with collective smoothing for solving the multiobjective optimality system discretized with finite elements. Error estimates for the optimal solution and two-grid local Fourier analysis of the multigrid scheme are presented. Results of numerical experiments are presented to demonstrate the effectiveness of the proposed framework.
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SARRAF, S. S., E. J. LOPEZ, G. A. RIOS RODRIGUEZ, and V. E. SONZOGNI. "A MULTIGRID METHOD FOR THE SOLUTION OF COMPOSITE MESH PROBLEMS." Latin American Applied Research - An international journal 45, no. 1 (January 30, 2015): 57–63. http://dx.doi.org/10.52292/j.laar.2015.373.

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The Composite Finite Element Mesh method is useful for the estimation of the discretization error and, in addition, for the nodal solution improvement with a small increase in the computational cost. The technique uses two meshes with different element size to discretize a given problem and, then, it redefines the resulting linear system. On the other hand, Multigrid methods solve a linear system using systems of several sizes resulting from a hierarchy of meshes. This feature motivates the study of the application of the Multigrid strategy together with the Composite Mesh technique. In this work, it is proposed a Multigrid method to solve problems where the Composite Mesh is applied. The goal of the proposal is to achieve both, the advantages of the Multigrid algorithm efficiency and the solution improvement given by the Composite Mesh technique. The new method is tested with some elliptic problems with analytical solution.
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Celestina, M. L., J. J. Adamczyk, and S. G. Rubin. "A Solution Strategy Based on Segmented Domain Decomposition Multigrid for Turbomachinery Flows." Journal of Turbomachinery 124, no. 3 (July 1, 2002): 341–50. http://dx.doi.org/10.1115/1.1451085.

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A Segmented Domain Decomposition Multigrid (SDDMG) procedure was developed for viscous flow problems as they apply to turbomachinery flows. The procedure divides the computational domain into a coarse mesh comprised of uniformly spaced cells. To resolve smaller length scales such as the viscous layer near a surface, segments of the coarse mesh are subdivided into a finer mesh. This is repeated until adequate resolution of the smallest relevant length scale is obtained. Multigrid is used to communicate information between the different grid levels [1]. To test the procedure, simulation results will be presented for a compressor and turbine cascade. These simulations are intended to show the ability of the present method to generate grid independent solutions. Comparisons with data will also be presented. These comparisons will further demonstrate the usefulness of the present work for they allow an estimate of the accuracy of the flow modeling equations independent of error attributed to numerical discretization.
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Muzhinji, K., S. Shateyi, and S. S. Motsa. "The Mixed Finite Element Multigrid Method for Stokes Equations." Scientific World Journal 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/460421.

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The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-TaylorQ2-Q1pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
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CIEGIS, R., F. GASPAR, and C. RODRIGO. "On The Parallel Multiblock Geometric Multigrid Algorithm." Computational Methods in Applied Mathematics 8, no. 3 (2008): 223–36. http://dx.doi.org/10.2478/cmam-2008-0016.

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Abstract The application of a parallel multiblock geometric multigrid is consid-ered. It is applied to solve a two-dimensional poroelastic model. This system of PDEs is approximated by a special stabilized monotone finite-difference scheme. The obtained system of linear algebraic equations is solved by a multigrid method, when a domain is partitioned into structured blocks. A new strategy for the solution of the discrete problem on the coarsest grid is proposed and the efficiency of the obtained algorithm is investigated. The geometrical structure of the sequential multigrid method is used to develop a parallel version of the multigrid algorithm. The convergence properties of several smoothers are investigated and some computational results are presented.
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Briesen, Heiko, and Wolfgang Marquardt. "Adaptive multigrid solution strategy for the dynamic simulation of petroleum mixture processes." Computers & Chemical Engineering 29, no. 1 (December 2004): 139–48. http://dx.doi.org/10.1016/j.compchemeng.2004.07.010.

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Borzì, A., and K. Kunisch. "A globalization strategy for the multigrid solution of elliptic optimal control problems." Optimization Methods and Software 21, no. 3 (June 2006): 445–59. http://dx.doi.org/10.1080/10556780500099944.

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Mowat, Andrew Gavin Bradford, Wilhelm Johann van den Bergh, Arnaud George Malan, and Daniel Wilke. "An AMG strategy for efficient solution of free-surface flows." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (May 3, 2016): 1172–86. http://dx.doi.org/10.1108/hff-09-2015-0389.

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Purpose – An area of great interest in current computational fluid dynamics research is that of free-surface modelling (FSM). Semi-implicit pressure-based FSM flow solvers typically involve the solution of a pressure correction equation. The latter being computationally intensive, the purpose of this paper is to involve the implementation and enhancement of an algebraic multigrid (AMG) method for its solution. Design/methodology/approach – All AMG components were implemented via object-oriented C++ in a manner which ensures linear computational scalability and matrix-free storage. The developed technology was evaluated in two- and three-dimensions via application to a dam-break test case. Findings – AMG performance was assessed via comparison of CPU cost to that of several other competitive sparse solvers. The standard AMG implementation proved inferior to other methods in three-dimensions, while the developed Freeze version achieved significant speed-ups and proved to be superior throughout. Originality/value – A so-called Freeze method was developed to address the computational overhead resulting from the dynamically changing coefficient matrix. The latter involves periodic AMG setup steps in a manner that results in a robust and efficient black-box solver.
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Hillewaert, Koen, Nicolas Chevaugeon, Philippe Geuzaine, and Jean-François Remacle. "Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations." International Journal for Numerical Methods in Fluids 51, no. 9-10 (2006): 1157–76. http://dx.doi.org/10.1002/fld.1135.

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Yang, Feng Wei, Chandrasekhar Venkataraman, Vanessa Styles, and Anotida Madzvamuse. "A Robust and Efficient Adaptive Multigrid Solver for the Optimal Control of Phase Field Formulations of Geometric Evolution Laws." Communications in Computational Physics 21, no. 1 (December 5, 2016): 65–92. http://dx.doi.org/10.4208/cicp.240715.080716a.

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AbstractWe propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution laws. The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility. Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focus on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problemis computationally challenging, requiring massive amounts of computational time and memory storage. The main focus of this work is to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An in-house two-grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptive-step gradient update for the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and efficiency. A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3-D which would be computationally infeasible without the solution strategies proposed in the present work.
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Dissertations / Theses on the topic "Multigrid solution strategy"

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Van, den Bergh Wilhelm J. "An algebraic multigrid solution strategy for efficient solution of free-surface flows." Diss., 2011. http://hdl.handle.net/2263/28124.

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Free-surface modelling (FSM) is a highly relevant and computationally intensive area of study in modern computational fluid dynamics. The Elemental software suite currently under development offers FSMcapability, and employs a preconditioned GMRES solver in an attempt to effect fast solution times. In terms of potential solver performance however, multigrid methods can be considered state-of-the-art. This work details the investigation into the use of AlgebraicMultigrid (AMG) as a high performance solver tool for use as black box plug-in for Elemental FSM. Special attention was given to the development of novel and robust methods of addressing AMG setup costs in addition to transcribing the solver to efficient C++ object-oriented code. This led to the development of the so-called Freeze extension of the basic algebraic multigrid method in an object-oriented C++ programming environment. The newly developed Freeze method reduces setup costs by periodically performing the setup procedure in an automatic and robust manner. The developed technology was evaluated in terms of robustness, stability and speed by applying it to benchmark FSM problems on structured and unstructured meshes of various sizes. This evaluation yielded a number of conclusive findings. First, the developed Freeze method reduced setup times by an order of magnitude. Second, the developed AMG solver offered substantial performance increases over the preconditioned GMRES method. In this way, it is proposed that this work has furthered the state-of-the-art of algebraic multigrid methods applied in the context of free-surface modelling.
Dissertation (MEng)--University of Pretoria, 2011.
Mechanical and Aeronautical Engineering
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Book chapters on the topic "Multigrid solution strategy"

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Briesen, Heiko, and Wolfgang Marquardt. "Adaptive multigrid solution strategy for the dynamic simulation of petroleum mixture processes: A case study." In Computer Aided Chemical Engineering, 406–9. Elsevier, 2003. http://dx.doi.org/10.1016/s1570-7946(03)80578-3.

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Conference papers on the topic "Multigrid solution strategy"

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Darbandi, Masoud, Gerry E. Schneider, and Arash Taheri. "Developing an Efficient Multigrid Strategy for Solving Incompressible Flow." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60710.

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In this work, a multigrid acceleration technique is suitably developed for solving the two-dimensional incompressible Navier-Stokes equations using an implicit finite element volume method. In this regard, the solution domain is broken into a huge number of quadrilateral finite elements. The accurate numerical solution of a flow field can be achieved if very fine grid resolutions are utilized. Unfortunately, the standard implicit solvers need more computational time to solve larger size of algebraic set of equations which normally arise if fine grid distributions are used. Past experience has shown that the convergence of classical relaxation schemes perform an initial rapid decrease of residuals followed by a slower rate of decrease. This point indicates that a relaxation procedure is efficient for eliminating only the high frequency components of the residuals. This problem can be overcome using multigrid method, i.e., carrying out the relaxation procedure on a series of different grid sizes. There are different prolongation operators to establish a multigrid procedure. A new prolongation expression is suitably developed in this work. It needs constructing data during refining and coarsening stages which is fulfilled using suitable finite element interpolators. The extended formulations are finally used to test several different problems with available benchmark solutions. The results indicate that the current multigrid strategy effectively improves the bandit solver performance.
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Celestina, M. L., J. J. Adamczyk, and S. G. Rubin. "A Solution Strategy Based on Segmented Domain Decomposition Multigrid for Turbomachinery Flows." In ASME Turbo Expo 2001: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/2001-gt-0435.

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A Segmented Domain Decomposition Multigrid (SDDMG) procedure was developed for viscous flow problems as they apply to turbomachinery flows. The procedure divides the computational domain into a coarse mesh comprised of uniformly spaced cells. To resolve smaller length scales such as the viscous layer near a surface, segments of the coarse mesh are subdivided into a finer mesh. This is repeated until adequate resolution of the smallest relevant length scale is obtained. Multigrid is used to communicate information between the different grid levels [1]. To test the procedure, simulation results will be presented for a compressor and turbine cascade. These simulations are intended to show the ability of the present method to generate grid independent solutions. Comparisons with data will also be presented. These comparisons will further demonstrate the usefulness of the present work for they allow an estimate of the accuracy of the flow modeling equations independent of error attributed to numerical discretization.
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Zwart, Philip J., Alan D. Burns, and Paul F. Galpin. "Coupled Algebraic Multigrid for Free Surface Flow Simulations." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29080.

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An accurate, efficient algorithm for solving free surface flows with ANSYS CFX is described. Accuracy is achieved using a compressive advection discretization which maintains a sharp free surface interface representation without relying on a small timestep. Efficiency is obtained using a solution algorithm which implicitly couples velocity, pressure, and volume fractions in the same matrix, and solves these equations using algebraic multigrid. This coupled strategy overcomes difficulties encountered with segregated volume fraction algorithms, where heavy underrelaxation and long solution times are required. The resulting solution algorithm is scalable, leading to solution times which increase linearly with mesh size.
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Lygidakis, Georgios N., and Ioannis K. Nikolos. "Assessment of the Academic CFD Code “Galatea” Using the NASA Common Research Model (CRM)." In ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/esda2014-20265.

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CFD (Computational Fluid Dynamics) algorithms are nowadays a necessary tool in the aerospace science, as their application allows for the prediction of the aerodynamic characteristics of complete aircraft configurations in a relatively short period of time. A brief presentation and evaluation of such a recently developed academic code, named Galatea, is the main goal of this study. Galatea employs the Reynolds Averaged Navier-Stokes (RANS) equations, discretized with a node-centered finite-volume scheme on three-dimensional unstructured hybrid grids for the simulation of inviscid and viscous compressible fluid flows. For the turbulence prediction appropriate turbulence models (k-ε, k-ω and SST) have been incorporated, while for the acceleration of the solution an agglomeration multigrid scheme along with a suitable parallelization strategy are employed. For the assessment of this algorithm runs over the wing-body and the wing-body-horizontal tail NASA Common Research Model (CRM) configurations were performed, allowing for a comparison in terms of accuracy of the obtained results with the experimental wind tunnel data, as well as with the computational results of corresponding reference solvers.
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Rabi, Jose, and Marcelo de Lemos. "The effects of Peclet number and cycling strategy on multigrid numerical solutions of conductive-convective problems." In 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1998. http://dx.doi.org/10.2514/6.1998-2584.

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Strofylas, Giorgos A., Georgios N. Lygidakis, and Ioannis K. Nikolos. "Accelerating RBF-Based Mesh Deformation by Implementing an Agglomeration Strategy." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50902.

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During the past decade Radial Basis Functions-based mesh deformation techniques have been emerged as an indispensable tool of numerical simulations entailing grid transformation. Despite their important contribution to such problems, they suffer from a significant drawback; they call for relatively excessive memory and computation time requirements. A remedy to this deficiency seems to be the selection of a reduced set of surface nodes, to be used as RBF’s centers; an equations’ system with decreased dimensions is obtained in that way. In this paper a new methodology for such a reduced surface point selection is proposed, considering agglomeration of surface nodes’ control volumes. It relies on the strategy followed by the corresponding multigrid methods aiming to accelerate numerical solutions of fluid flow, radiative heat transfer, etc., problems. The developed merging procedure resembles the advancing front technique, as it begins from regions with surface discontinuities extending successively to the rest of the boundary domain. The proposed algorithm is assessed against a test case considering parabolic deformation of the wing of the DLR-F6 aircraft model; its potential to effectively generate deformed grids in terms of accuracy and efficiency is demonstrated, despite the notable reduction of RBF’s centers.
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Borello, D., and F. Rispoli. "Improved Non-Equilibrium Turbulence Closure Modeling for Axial Flow Compressors Simulation." In ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/gt2003-38672.

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The present paper investigates the predictive attitude of three non conventional turbulence closures in simulating the physics pertinent to decelerating turbomachinery flows. The performance of a cubic k-ε model and an algebraic Reynolds stress model adopting a non-linear link between turbulence and velocity gradients have been exploited with reference to their capabilities in predicting anisotropy effects and the sensibility to streamlines curvature. In addition, a modification of the kinetic energy production term in standard isotropic model has been also tested, in accord with Kato and Launder formulation. To put in evidence the predictive capabilities of such models a comparison with the standard Launder and Sharma turbulence closure will be carried out. The authors adopt a multi-level parallel solver developed in the framework of a finite element (FE) method based on a stabilized Petrov-Galerkin formulation. The FE method is here applied on mixed Q2-Q1 element shape functions. The solution scheme is based on a Multigrid (MG) solver properly developed to operate in a parallel environment. To increase the performance of MG schemes in solving self-adjoint elliptic problems a remedial strategy consisting of a LFMG-type scheme named Hybrid Linear Full Multi-Grid technique (HLFMG) has been proposed. The parallel algorithm follows a Single Program Multiple Domains (SPMD) scheme. The subdomains fields for Reynolds Averaged Navier-Stokes problem are generated by the adoption of an original overlapping domain decomposition technique. In the present paper we analyze a two-dimensional leading edge and both a DCA (2D) and NACA65 (3D) compressor cascades. The flows considered for model benchmarking are highly challenging because of the possibly transitional nature of the flow and the existence of three-dimensional phenomena and of significant separation regions. The potential of non-standard closures has been investigated in terms of both velocity and turbulent variables. In the leading edge test-case, the cubic k-ε model is shown to provide a better base-line for nonequilibrium effects simulation with respect to the algebraic stress model. The Kato and Launder modification has shown poor predictive attitude in representing the flow downstream the impingement and it has not adopted for the other test-cases. In the DCA simulation the presence of large transition regions leads to a degradation of the predictions of the cubic model. Algebraic stress model has shown performances comparable to the cubic model ones. The 3D linear cascade flow simulations put in evidence that the standard and algebraic Reynolds stress approaches have similar performance, clearly worse respect to the cubic model.
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