Algebraic Multigrid Block Triangular Preconditioning for Multidimensional Three-Temperature Radiation Diffusion Equations

2021 ◽  
Vol 13 (5) ◽  
pp. 1203-1226
Author(s):  
global sci
Keyword(s):  
Algebraic Multigrid ◽  
Diffusion Equations ◽  
Radiation Diffusion ◽  
Temperature Radiation

UA-AMG Methods for 2-D 1-T Radiation Diffusion Equations and Their CPU-GPU Implementations

2013 ◽  
Author(s):  
Xiaoqiang Yue ◽  
Shi Shu ◽  
Chunsheng Feng
Keyword(s):  
Graphics Processing Units ◽  
Diffusion Equations ◽  
Radiation Diffusion ◽  
Smoothed Aggregation ◽  
Single Temperature ◽  
Initial Mesh ◽  
Finite Volume Element ◽  
Temperature Radiation ◽  
Graphics Processing ◽  
Different Characteristics

In this paper, we study several unsmoothed aggregation based algebraic multigrid (UA-AMG) methods with regard to different characteristics of CPUs and graphics processing units (GPUs). We propose some UA-AMG methods with lower computational complexity for CPU and CPU-GPU, and study these UA-AMG methods mixing with 4 kinds of red-black colored Gauss-Seidel smoothers for CPU-GPU since the initial mesh is structured. These UA-AMG methods are used as preconditioners for the conjugate gradient (CG) solver to solve a class of two-dimensional single-temperature radiation diffusion equations discretized by preserving symmetry finite volume element scheme. Numerical results demonstrate that, UA-NA-CG-s, which wins the best robustness and efficiency among them, is much more efficient than the default AMG preconditioned CG solvers in HYPRE, AGMG and Cusp for CPU; Under CPU-GPU, UA-W-CG-p is the most robust and efficient one, and rather more efficient than the smoothed aggregation based AMG preconditioned CG solver in Cusp.

An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

2015 ◽  
Vol 18 (5) ◽  
pp. 1313-1335 ◽  
Author(s):  
Xiaoqiang Yue ◽  
Shi Shu ◽  
Xiao wen Xu ◽  
Zhiyang Zhou
Keyword(s):  
Convergence Analysis ◽  
Estimation Theory ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Condition Numbers ◽  
Radiation Diffusion ◽  
Discrete Problems ◽  
Preconditioned Gmres

AbstractThe paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

scholarly journals Analysis of algebraic multigrid parameters for two-dimensional steady-state heat diffusion equations

2012 ◽  
Vol 36 (7) ◽  
pp. 2996-3006 ◽  
Author(s):  
R. Suero ◽  
M.A.V. Pinto ◽  
C.H. Marchi ◽  
L.K. Araki ◽  
A.C. Alves
Keyword(s):  
Steady State ◽  
Algebraic Multigrid ◽  
Heat Diffusion ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
State Heat ◽  
Steady State Heat
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