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Автор: Grafiati
Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Adaptive Multigrid"

1

Brezina, M., R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge. "Adaptive Algebraic Multigrid." SIAM Journal on Scientific Computing 27, no. 4 (January 2006): 1261–86. http://dx.doi.org/10.1137/040614402.

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2

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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3

Bittencourt, Marco L., Craig C. Douglas, and Raúl A. Feijóo. "Adaptive non‐nested multigrid methods." Engineering Computations 19, no. 2 (March 2002): 158–76. http://dx.doi.org/10.1108/02644400210419030.

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4

Bartsch, Guido, and Christian Wulf. "Adaptive Multigrid for Helmholtz Problems." Journal of Computational Acoustics 11, no. 03 (September 2003): 341–50. http://dx.doi.org/10.1142/s0218396x03001997.

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Анотація:
Solving Helmholtz problems for low frequency sound fields by a truncated modal basis approach is very efficient. The most time-consuming process is the calculation of the undamped modes. Using traditional FE solvers, the user has to provide a mesh which has at least six nodes per wavelength in each spatial direction to achieve acceptable results. Because the mesh size increases with the 3rd power of the highest frequency of interest, this uniform dense mesh approach is a very expensive way of creating a modal space. However, the number of modes and the accuracy of the modal basis directly influences the solution quality. It is well known that the representation of sound fields by modal basis functions φi is optimal with respect to the L2 error norm. This means that having a modal basis Φ := {φi, i = 1⋯n}, the distance between true and approximated sound field takes its minimum in the mean square. So, it is necessary to have a FE basis which also minimizes the discretization error when computing the modal basis. One can reach this goal by applying adaptive mesh refinements. Additionally, this yields the opportunity of using fast multigrid methods to solve discrete eigenvalue problems. In context of this presentation we will discuss the results of our adaptive multigrid algorithms.
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5

Belouafi, M. E., M. Beggas, and M. Haiour. "MAXIMUM NORM CONVERGENCE OF NEWTON-MULTIGRID METHODS FOR ELLIPTIC QUASI-VARIATIONAL INEQUALITIES WITH NONLINEAR SOURCE TERMS." Advances in Mathematics: Scientific Journal 11, no. 10 (October 29, 2022): 969–83. http://dx.doi.org/10.37418/amsj.11.10.12.

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In this paper, Newton-multigrid scheme on adaptive finite element discretisation is employed for solving elliptic quasi-variational inequalities with nonlinear source terms. We use Newton’s method as the outer iteration for the standard linearization, and using standard multigrid as the inner iteration for the solution of the Jacobian system at each step. The uniform convergence of Newton-multigrid methods is shown in the sense that the multigrid methods have a contraction number with respect to the maximum norm.
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6

Wada, Yoshitaka, Takuji Hayashi, Masanori Kikuchi, and Fei Xu. "Improvement of Unstructured Quadrilateral Mesh Quality for Multigrid Analysis." Advanced Materials Research 33-37 (March 2008): 833–38. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.833.

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Due to more complex and severe design restrictions, more effective and faster finite element analyses are demanded. There are several ways to compute FE analysis efficiently: parallel computing, fast iterative or direct solvers, adaptive analysis and so on. One of the most effective analysis ways is the combination of adaptive analysis and multigrid iterative solver, because an adaptive analysis requires several meshes with difference resolutions and multigrid solver utilizes such meshes to accelerate its computation. However, convergence of multigrid solver is largely affected by initial shape of each element. An effective mesh improvement method is proposed here. It is the combination of mesh coarsening and refinement. A good mesh can be obtained by the method to be applied to an initial mesh, and better convergence is achieved by the improved initial mesh.
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Brezina, M., R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge. "Adaptive Smoothed Aggregation ($\alpha$SA) Multigrid." SIAM Review 47, no. 2 (January 2005): 317–46. http://dx.doi.org/10.1137/050626272.

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Nägel, Arne, Robert D. Falgout, and Gabriel Wittum. "Filtering algebraic multigrid and adaptive strategies." Computing and Visualization in Science 11, no. 3 (March 6, 2007): 159–67. http://dx.doi.org/10.1007/s00791-007-0066-9.

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Bastian, Peter. "Load Balancing for Adaptive Multigrid Methods." SIAM Journal on Scientific Computing 19, no. 4 (July 1998): 1303–21. http://dx.doi.org/10.1137/s1064827596297562.

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Zheng, Y., and L. He. "Multigrid upwind Euler/Navier-Stokes computation on adaptive unstructured meshes." Aeronautical Journal 105, no. 1046 (April 2001): 173–84. http://dx.doi.org/10.1017/s0001924000025410.

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Abstract An unstructured flow solver with adaptive mesh refinement and multigrid acceleration is developed to efficiently compute two-dimensional inviscid and viscous steady flows about complex configurations. High resolution is achieved by using the upwind scheme coupled with adaptive mesh refinement. An aspect-ratio adaptive multigrid method is developed and applied to effectively accelerate the solution convergence of the explicit time-marching in the near wall regions with high aspect mesh ratios. Numerical examples are presented for configurations and conditions ranging from transonic to low speed flows to demonstrate accuracy, speed, and robustness of the method.
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Дисертації з теми "Adaptive Multigrid"

1

Brannick, James. "Adaptive algebraic multigrid coarsening strategies." Diss., Connect to online resource, 2005. http://wwwlib.umi.com/cr/colorado/fullcit?p3190384.

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2

Mayfield, Andrew James. "Adaptive mesh refinement." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358687.

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Kahl, Karsten. "Adaptive Algebraic Multigrid Methods for Lattice QCD Computations." Wuppertal Universitätsbibliothek Wuppertal, 2010. http://d-nb.info/1000531767/34.

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Rottmann, Matthias [Verfasser]. "Adaptive Domain Decomposition Multigrid for Lattice QCD / Matthias Rottmann." Wuppertal : Universitätsbibliothek Wuppertal, 2016. http://d-nb.info/1093603240/34.

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5

Thorne, Jr Daniel Thomas. "Multigrid with Cache Optimizations on Adaptive Mesh Refinement Hierarchies." UKnowledge, 2003. http://uknowledge.uky.edu/gradschool_diss/325.

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This dissertation presents a multilevel algorithm to solve constant and variable coeffcient elliptic boundary value problems on adaptively refined structured meshes in 2D and 3D. Cacheaware algorithms for optimizing the operations to exploit the cache memory subsystem areshown. Keywords: Multigrid, Cache Aware, Adaptive Mesh Refinement, Partial Differential Equations, Numerical Solution.
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6

Kahl, Karsten [Verfasser]. "Adaptive Algebraic Multigrid Methods for Lattice QCD Computations / Karsten Kahl." Wuppertal : Universitätsbibliothek Wuppertal, 2010. http://d-nb.info/1000531767/34.

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7

Vey, Simon. "Adaptive Finite Elements for Systems of PDEs: Software Concepts, Multi-level Techniques and Parallelization." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1212489177096-59154.

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Анотація:
In the recent past, the field of scientific computing has become of more and more importance for scientific as well as for industrial research, playing a comparable role as experiment and theory do. This success of computational methods in scientific and engineering research is next to the enormous improvement of computer hardware to a large extend due to contributions from applied mathematicians, who have developed algorithms which make real life applications feasible. Examples are adaptive methods, high order discretization, fast linear and non-linear solvers and multi-level methods. The application of these methods in a large class of problems demands for suitable and robust tools for a flexible and efficient implementation. In order to play a crucial role in scientific and engineering research, besides efficiency in the numerical solution, also efficiency in problem setup and interpretation of simulation results is of utmost importance. As modeling and computing comes closer together, efficient computational methods need to be applied to new sets of equations. The problems to be addressed by simulation methods become more and more complicated, ranging over different scales, interacting on different dimensions and combining different physics. Such problems need to be implemented in a short period of time, solved on complicated domains and visualized with respect to the demand of the user. %Only a modular abstract simulation environment will fulfill these requirements and allow to setup, solve and visualize real-world problems appropriately. In this work, the concepts and the design of the C++ finite element toolbox AMDiS (adaptive multidimensional simulations) are described. It is shown, how abstract data structures and modern software concepts can help to design user-friendly finite element software, which provides large flexibility in problem definition while on the other hand efficiently solves these problems. Also systems of coupled problems can be solved in an intuitive way. In order to demonstrate its possibilities, AMDiS has been applied to several non-standard problems. The most time-consuming part in most simulations is the solution of linear systems of equations. Multi-level methods use discretization hierarchies to solve these systems in a very efficient way. In AMDiS, such multi-level techniques are implemented in the context of adaptive finite elements. Several numerical results are given which compare this multigrid solver with classical iterative methods. Besides the development of more efficient algorithms also the growing hardware capabilities lead to an improvement of simulation possibilities. Modern computing clusters contain more and more processors and also personal computers today are often equipped with multi-core processors. In this work, a new parallelization approach has been developed which allows the parallelization of sequential code in a very easy way and reduces the communication overhead compared to classical parallelization concepts.
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8

Rosam, Jan. "A fully implicit, fully adaptive multigrid method for multiscale phase-field modelling." Thesis, University of Leeds, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.445357.

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9

Sanders, Geoffrey D. "Extensions to adaptive smooth aggregation (alphaSA) multigrid: Eigensolver initialization and nonsymmetric problems." Connect to online resource, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3337216.

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10

Vey, Simon. "Adaptive Finite Elements for Systems of PDEs: Software Concepts, Multi-level Techniques and Parallelization." Doctoral thesis, Technische Universität Dresden, 2007. https://tud.qucosa.de/id/qucosa%3A23684.

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Анотація:
In the recent past, the field of scientific computing has become of more and more importance for scientific as well as for industrial research, playing a comparable role as experiment and theory do. This success of computational methods in scientific and engineering research is next to the enormous improvement of computer hardware to a large extend due to contributions from applied mathematicians, who have developed algorithms which make real life applications feasible. Examples are adaptive methods, high order discretization, fast linear and non-linear solvers and multi-level methods. The application of these methods in a large class of problems demands for suitable and robust tools for a flexible and efficient implementation. In order to play a crucial role in scientific and engineering research, besides efficiency in the numerical solution, also efficiency in problem setup and interpretation of simulation results is of utmost importance. As modeling and computing comes closer together, efficient computational methods need to be applied to new sets of equations. The problems to be addressed by simulation methods become more and more complicated, ranging over different scales, interacting on different dimensions and combining different physics. Such problems need to be implemented in a short period of time, solved on complicated domains and visualized with respect to the demand of the user. %Only a modular abstract simulation environment will fulfill these requirements and allow to setup, solve and visualize real-world problems appropriately. In this work, the concepts and the design of the C++ finite element toolbox AMDiS (adaptive multidimensional simulations) are described. It is shown, how abstract data structures and modern software concepts can help to design user-friendly finite element software, which provides large flexibility in problem definition while on the other hand efficiently solves these problems. Also systems of coupled problems can be solved in an intuitive way. In order to demonstrate its possibilities, AMDiS has been applied to several non-standard problems. The most time-consuming part in most simulations is the solution of linear systems of equations. Multi-level methods use discretization hierarchies to solve these systems in a very efficient way. In AMDiS, such multi-level techniques are implemented in the context of adaptive finite elements. Several numerical results are given which compare this multigrid solver with classical iterative methods. Besides the development of more efficient algorithms also the growing hardware capabilities lead to an improvement of simulation possibilities. Modern computing clusters contain more and more processors and also personal computers today are often equipped with multi-core processors. In this work, a new parallelization approach has been developed which allows the parallelization of sequential code in a very easy way and reduces the communication overhead compared to classical parallelization concepts.
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Книги з теми "Adaptive Multigrid"

1

Institute for Computer Applications in Science and Engineering., ed. Multigrid solution strategies for adaptive meshing problems. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1995.

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2

Predovic, D. Tom. Multigrid solution of the Euler equations using unstructured adaptive meshes. [Downsview, Ont.]: University of Toronto, Dept. of Aerospace Science and Engineering, 1994.

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3

Stals, Linda. The solution of radiation transport equations with adaptive finite elements. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2001.

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4

B, Baden Scott, ed. Structured adaptive mesh refinement (SAMR) grid methods. New York: Springer, 2000.

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5

1934-, Jameson Antony, and Langley Research Center, eds. Multigrid solution of the Euler equations on unstructured and adaptive meshes. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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6

Kornhuber, Ralf. Adaptive monotone multigrid methods for nonlinear variational problems: Von Ralf Kornhuber. Stuttgart: B.G. Teubner, 1997.

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7

Mavriplis, Dimitri J. Multigrid solution of the Euler equations on unstructured and adaptive meshes. Hampton, Va: ICASE, 1987.

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8

Mavriplis, Dimitri J. Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes. Hampton, Va: ICASE, 1988.

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9

R, Blake Kenneth, and United States. National Aeronautics and Space Administration., eds. Multigrid solution of internal flows using unstructured solution adaptive meshes: Final report. [Washington, DC: National Aeronautics and Space Administration, 1992.

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10

Mavriplis, Dimitri J. Zonal multigrid solution of compressible flow problems on unstructured and adaptive meshes. Hampton, Va: ICASE, 1989.

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Частини книг з теми "Adaptive Multigrid"

1

Rüde, U. "Adaptive Higher Order Multigrid Methods." In Multigrid Methods III, 339–51. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-5712-3_25.

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2

Ritzdorf, Hubert, and Klaus Stüben. "Adaptive Multigrid on Distributed Memory Computers." In Multigrid Methods IV, 77–95. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8524-9_6.

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3

Bastian, P., and G. Wittum. "On Robust and Adaptive Multi-Grid Methods." In Multigrid Methods IV, 1–17. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8524-9_1.

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4

Michelsen, J. A. "Mesh-Adaptive Solution of the Navier-Stokes Equations." In Multigrid Methods III, 301–12. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-5712-3_22.

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5

Catalano, L. A., P. De Palma, M. Napolitano, and G. Pascazio. "A Multidimensional Upwind Solution Adaptive Multigrid Solver for Inviscid Cascades." In Multigrid Methods IV, 151–62. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8524-9_11.

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6

Baiardi, Fabrizio, Sarah Chiti, Paolo Mori, and Laura Ricci. "Adaptive Multigrid Methods in MPI." In Recent Advances in Parallel Virtual Machine and Message Passing Interface, 80–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-45255-9_14.

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7

De Keyser, J., and D. Roose. "Parallel Steady Euler Calculations using Multigrid Methods and Adaptive Irregular Meshes." In Multigrid Methods IV, 163–74. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8524-9_12.

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Hemker, P. W., and J. Molenaar. "An adaptive multigrid approach for the solution of the 2D semiconductor equations." In Multigrid Methods III, 41–60. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-5712-3_3.

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9

Ginzburg, I., G. Wittum, and S. Zaleski. "Adaptive Multigrid Computations of Multiphase Flows." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), 77–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-45693-3_5.

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Bastian, P., and G. Wittum. "Adaptive Multigrid Methods: The UG Concept." In Notes on Numerical Fluid Mechanics (NNFM), 17–37. Wiesbaden: Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-663-14246-1_2.

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Тези доповідей конференцій з теми "Adaptive Multigrid"

1

Zhao, Bo, Huaxiang Wang, Li Hu, L. Xu, and Y. Yan. "An Adaptive Multigrid Method For EIT." In 2007 IEEE Instrumentation & Measurement Technology Conference IMTC 2007. IEEE, 2007. http://dx.doi.org/10.1109/imtc.2007.379236.

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2

Maple, Raymond. "Multigrid for Adaptive Harmonic Balance CFD." In 16th AIAA Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-3434.

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3

Wettig, Tilo, Simon Heybrock, Matthias Rottmann, and Peter Georg. "Adaptive algebraic multigrid on SIMD architectures." In The 33rd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.251.0036.

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Watanabe, Kota, Seiji Fujino, and Hajime Igarashi. "Multigrid method with adaptive IDR-based Jacobi Smoother." In 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2010). IEEE, 2010. http://dx.doi.org/10.1109/cefc.2010.5481751.

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Parthasarathy, Vijayan, and Y. Kallinderis. "A new multigrid approach for 3D unstructured, adaptive grids." In 32nd Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1994. http://dx.doi.org/10.2514/6.1994-78.

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Dadone, A., and P. DePalma. "An adaptive multigrid upwind solver for compressible viscous flows." In Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1995. http://dx.doi.org/10.2514/6.1995-2181.

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Abdul-Halim, M., and A. Tourlidakis. "Euler solutions on adaptive unstructured grids using simple multigrid." In 14th Applied Aerodynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-2424.

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Zhu, Zhengyong, Bo Yao, and Chung-Kuan Cheng. "Power network analysis using an adaptive algebraic multigrid approach." In the 40th conference. New York, New York, USA: ACM Press, 2003. http://dx.doi.org/10.1145/775832.775862.

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Santos Conde, J. E., A. Teuner, and B. J. Hosticka. "Hierarchical locally adaptive multigrid motion estimation for surveillance applications." In 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258). IEEE, 1999. http://dx.doi.org/10.1109/icassp.1999.757563.

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Bigarella, Enda, Edson Basso, and Joao Azevedo. "Multigrid Adaptive-Mesh Turbulent Simulations of Launch Vehicle Flows." In 21st AIAA Applied Aerodynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-4076.

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Звіти організацій з теми "Adaptive Multigrid"

1

Fulton, Scott R. Adaptive Multigrid Hurricane Modeling. Fort Belvoir, VA: Defense Technical Information Center, September 1999. http://dx.doi.org/10.21236/ada630375.

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Fulton, Scott R. An Adaptive Multigrid Barotropic Tropical Cyclone Track Model. Fort Belvoir, VA: Defense Technical Information Center, December 1999. http://dx.doi.org/10.21236/ada376987.

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3

Kalchev, D. Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients. Office of Scientific and Technical Information (OSTI), April 2012. http://dx.doi.org/10.2172/1047794.

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Fulton, Scott R., Nicole M. Burgess, and Brittany L. Mitchell. Experiments With a Self-Adaptive Multigrid Barotropic Tropical Cyclone Track Model. Fort Belvoir, VA: Defense Technical Information Center, January 1999. http://dx.doi.org/10.21236/ada376800.

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McCormick, Stephen. Algebraic Multigrid and the Fast Adaptive Composite Grid Method in Large Scale Computation. Fort Belvoir, VA: Defense Technical Information Center, February 1986. http://dx.doi.org/10.21236/ada183061.

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Hu, Miao, and Scott R. Fulton. Comparison of Discretization Accuracy in an Adaptive Multigrid Barotropic Tropical Cyclone Track Model. Fort Belvoir, VA: Defense Technical Information Center, May 2000. http://dx.doi.org/10.21236/ada377011.

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7

Brannick, J. Final Report on Subcontract B635759: Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers. Office of Scientific and Technical Information (OSTI), April 2021. http://dx.doi.org/10.2172/1781295.

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