Results 1 to 10 of about 481 (184)
Research of the Algebraic Multigrid Method for Electron Optical Simulator [PDF]
Entropy, 2022 At present, electron optical simulator (EOS) takes a long time to solve linear FEM systems. The algebraic multigrid preconditioned conjugate gradient (AMGPCG) method can improve the efficiency of solving systems.
Zhi Wang +7 more
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An introduction to algebraic multigrid [PDF]
Computing in Science and Engineering, 2006 Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical ...
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Compatible Relaxation and Coarsening in Algebraic Multigrid [PDF]
SIAM Journal of Scientific Computing, 2010 We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection.
James Brannick, Robert D Falgout
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XAMG: A library for solving linear systems with multiple right-hand side vectors
SoftwareX, 2021 This paper presents the XAMG library for solving large sparse systems of linear algebraic equations with multiple right-hand side vectors. The library specializes, but is not limited, to the solution of linear systems obtained from the discretization of ...
Boris Krasnopolsky, Alexey Medvedev
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Algebraic multigrid methods [PDF]
Acta Numerica, 2017 This paper provides an overview of AMG methods for solving large-scale systems of equations, such as those from discretizations of partial differential equations. AMG is often understood as the acronym of ‘algebraic multigrid’, but it can also be understood as ‘abstract multigrid’. Indeed, we demonstrate in this paper how and why an algebraic multigrid
Jinchao Xu, Ludmil T. Zikatanov
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Mathematics, 2023 In this paper, we examine deflation-based algebraic multigrid methods for solving large systems of linear equations. Aggregation of the unknown terms is applied for coarsening, while deflation techniques are proposed for improving the rate of convergence.
Anastasia A. Natsiou +3 more
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3-D radiative transfer in large-eddy simulations – experiences coupling the TenStream solver to the UCLA-LES [PDF]
Geoscientific Model Development, 2016 The recently developed 3-D TenStream radiative transfer solver was integrated into the University of California, Los Angeles large-eddy simulation (UCLA-LES) cloud-resolving model.
F. Jakub, B. Mayer
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Algebraic Multigrid for Markov Chains [PDF]
SIAM Journal on Scientific Computing, 2010 An algebraic multigrid (AMG) method is presented for the calculation of the stationary probability vector of an irreducible Markov chain. The method is based on standard AMG for nonsingular linear systems, but in a multiplicative, adaptive setting. A modified AMG interpolation formula is proposed that produces a nonnegative interpolation operator with ...
Hans De Sterck +5 more
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Generalizing reduction‐based algebraic multigrid
Numerical Linear Algebra with Applications, 2023 AbstractAlgebraic multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their performance.
Tareq Uz Zaman +5 more
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Effective Preconditioners for Mixed‐Dimensional Scalar Elliptic Problems
Water Resources Research, 2023 Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed‐dimensional scalar elliptic
Xiaozhe Hu +2 more
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