Multigrid methods with applications to reservoir simulation

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Multigrid methods are studied for solving elliptic partial differential equations. Focus is on parallel multigrid methods and their use for reservoir simulation. Multicolor Fourier analysis is used to analyze the behavior of standard multigrid methods for problems in one and two dimensions. Relation between multicolor and standard Fourier analysis is established. Multiple coarse grid methods for solving model problems in 1 and 2 dimensions are considered; at each coarse grid level we use more than one coarse grid to improve convergence. For a given Dirichlet problem, a related extended problem is first constructed; a purification procedure can be used to ... continued below

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246 p.

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Xiao, Shengyou May 1, 1994.

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Description

Multigrid methods are studied for solving elliptic partial differential equations. Focus is on parallel multigrid methods and their use for reservoir simulation. Multicolor Fourier analysis is used to analyze the behavior of standard multigrid methods for problems in one and two dimensions. Relation between multicolor and standard Fourier analysis is established. Multiple coarse grid methods for solving model problems in 1 and 2 dimensions are considered; at each coarse grid level we use more than one coarse grid to improve convergence. For a given Dirichlet problem, a related extended problem is first constructed; a purification procedure can be used to obtain Moore-Penrose solutions of the singular systems encountered. For solving anisotropic equations, semicoarsening and line smoothing techniques are used with multiple coarse grid methods to improve convergence. Two-level convergence factors are estimated using multicolor. In the case where each operator has the same stencil on each grid point on one level, exact multilevel convergence factors can be obtained. For solving partial differential equations with discontinuous coefficients, interpolation and restriction operators should include information about the equation coefficients. Matrix-dependent interpolation and restriction operators based on the Schur complement can be used in nonsymmetric cases. A semicoarsening multigrid solver with these operators is used in UTCOMP, a 3-D, multiphase, multicomponent, compositional reservoir simulator. The numerical experiments are carried out on different computing systems. Results indicate that the multigrid methods are promising.

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246 p.

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OSTI as DE97000850

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  • Other Information: TH: Thesis

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  • Other: DE97000850
  • Report No.: DOE/ER/25183--T3
  • Report No.: CNA--265
  • Grant Number: FG03-93ER25183
  • Office of Scientific & Technical Information Report Number: 418388
  • Archival Resource Key: ark:/67531/metadc685905

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  • May 1, 1994

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  • July 25, 2015, 2:20 a.m.

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  • Nov. 5, 2015, 12:58 p.m.

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Xiao, Shengyou. Multigrid methods with applications to reservoir simulation, thesis or dissertation, May 1, 1994; United States. (digital.library.unt.edu/ark:/67531/metadc685905/: accessed September 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.