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A black-box iterative solver based on a two-level Schwarz method
Marian Brezina,Petr Vaněk +1 more
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TLDR
A black-box parallel iterative method suitable for solving both elliptic and certain non-elliptic problems discretized on unstructured meshes is proposed and the validity of the proved convegence estimate is confirmed.Abstract:
We propose a black-box parallel iterative method suitable for solving both elliptic and certain non-elliptic problems discretized on unstructured meshes. The method is analyzed in the case of the second order elliptic problems discretized on quasiuniform P1 and Q1 finite element meshes. The numerical experiments confirm the validity of the proved convegence estimate and show that the method can successfully be used for more difficult problems (e.g. plates, shells and Helmholtz equation in high-frequency domain.)read more
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Convergence of Algebraic Multigrid Based on Smoothed Aggregation II: Extension to a Petrov-Galerkin Method
TL;DR: In this paper, the authors give a convergence estimate for a Petrov-Galerkin Algebraic Multigrid method, where the prolongations are defined using the concept of smoothed aggregation while the restrictions are simple aggregation operators.
Journal ArticleDOI
Convergence of Algebraic Multigrid Based on Smoothed Aggregation
TL;DR: An abstract convergence estimate is proved for the Algebraic Multigrid Method with prolongator defined by a disaggregation followed by a smoothing of the problem matrix and a matrix of the zero energy modes of the same problem but with natural boundary conditions.
Journal ArticleDOI
Adaptive Smoothed Aggregation ($\alpha$SA) Multigrid
M. Brezina,Robert D. Falgout,Scott MacLachlan,Thomas A. Manteuffel,Stephen F. McCormick,John W. Ruge +5 more
TL;DR: An extension of the SA method in which good convergence properties are achieved in situations where explicit knowledge of the near-kernel components is unavailable is introduced in an adaptive process that uses the method itself to determine near- kernel components and adjusts the coarsening processes accordingly.
Journal ArticleDOI
Adaptive Smoothed Aggregation ($\alpha$SA)
Marian Brezina,Robert D. Falgout,Scott MacLachlan,Thomas A. Manteuffel,Stephen F. McCormick,J. Ruge +5 more
TL;DR: This paper introduces an extension of the SA method in which good convergence properties are achieved in situations where explicit knowledge of the near-nullspace components is unavailable, by using the method itself to determine near- nullspace components and adjusting the coarsening processes accordingly.
Journal ArticleDOI
Computational engineering and science methodologies for modeling and simulation of subsurface applications
TL;DR: This work overviews both basic and widely recognized multiphase and multicomponent models and presents several simulation examples which reflect the experiences of the research group at the Center for Subsurface Modeling at The University of Texas at Austin.
References
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Journal ArticleDOI
Algebraic multigrid (AMG): experiences and comparisons
TL;DR: A special AMG algorithm will be presented, which yields an iterative method which exhibits a convergence behavior typical for multigrid methods.
Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG)
J. Ruge,K. Stueben +1 more
Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems
TL;DR: In this article, the main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables.
Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes
Tony F. Chan,Barry Smith +1 more
TL;DR: This paper considers the problem of generating a multilevel grid hierarchy when only a fine, unstructured grid is given and generates a sequence of coarser grids by first forming a maximal independent set of the graph of the grid or its dual and then applying a Cavendish type algorithm to form the coarser triangulation.