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Block algebraic multigrid algorithm and its implementation technology in reservoir simulation software

Author: LiWenJun
Tutor: SunJiaZuo
School: Institute of Software, Chinese Academy of Sciences
Course: Theoretical Computer Science and Software
Keywords: Multigrid algorithm Numerical Simulation Software Block algebra Algebraic multigrid Implementation techniques Smooth operator Solver Reservoir Coarse grid correction Multigrid methods
CLC: TP391.9
Type: PhD thesis
Year: 2001
Downloads: 285
Quote: 2
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Wenjun LiDirected by Prof. Jiachang SunThe contributions of this thesis mainly fall into two parts.The first part is the study of BAMG’s algorithm. It consists of severalparts as following:Based on the idea that Algebraic Multigrids should be the practically itera-tive methods. we gite the premise that several iterations with smoothing operator. instead of direct methods, are performed on the coarsest level. Then we havethe theorv of general convergence of AMG under this premise. It has three the-orems about the estimates of convergence factors for three kinds of v─cyclesrespectively, i.e.. one is smoothing is performed after the coarse grid correctionsteps. another is smoothing is done before the coarse grid correction steps, andthe other is smoothing is done both before and after the coarse grid correction.Then these theorems are extended to the those of Block AMG(BAMG) whichbecome the theories of general convergence of BAMG.To construct the effective block Algebraic Multigrid Algorithms, we divideblock srnoothing operators and block interpolation operators into two kinds ofoperators respectivelv: then we analyse several properties which two kinds blocksmoothing operators and block interpolation operators should satisfv for the the-orv of general convergence of BAMG, and prove that both of interpolation oper-ators can guarantee the uniformitv of grid operator’s essential properties in therecursive application of multi-level cycles.Construction of BAMG Algorithm mainly includes two parts: the setup ofthe BAMG’s components and the solving process. In the first part of BAMGalgorithnl. we provide block grid coarsening and block interpolation algorithms.The second part of BAMG algorithm is similar to that of standard Multigrid,i.e., solving process with block smoothing operators and V--cycle method.Numerical results show that these two BAMG algorithms are effective insolving the large scale isotropic problems.The second part is the application of its realizable techniques in oil reservoirnumerical simulation software .It has the fOllowing several parts’The structural characters of the matrix in the solver of large oil reservoir nu-merical simulation software are analysed; the relationship between grid’s matrixand well’s matrix are discussed quantitatively fOr construction of preconditioner.From the published papers, it can be concluded that the application of AMGtechnique into oil reservoir numerical simulation software is a new and creativeresearch work at present.The given oil reservoir numerical simulation software is large,compIicatedand highly efficient. It is very difficult in applying AMG into the softtvaresuccessfully in order to improve its total efficiency Firstly the correct techniqueline should be found,and all details of the solver and its related parts in thegiven oil reservoir numerical simulation software should be understood very well.In the end, many programming techniques of reducing the run time of the added’programmes should be used, and Blas technique should be used to optimize theprogrammes of numerical computaion parts.With successful application of AMG pre-dispose technique into the solver oflarge scale oil reservoir numerical simulation software 1 the efficiency of the solveris improved.The several numerical results coming from the computation of real problemsof DaQing oil field in China show that the new software with AMG pre-disposetechnique improves the efficiency of its solver, and reduce the wall time of theoriginal solver by 13.4%,l4.5%,23.1% and 66.5%. then the conclusions can bedrawed that .4MG pre-dispose technique is very effective in solving the largeconvergent problems.

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