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.

Finite Volume Element Methods for Two-Dimensional Three-Temperature Radiation Diffusion Equations

2016 ◽  
Vol 9 (3) ◽  
pp. 470-496 ◽  
Author(s):  
Yanni Gao ◽  
Xiukun Zhao ◽  
Yonghai Li
Keyword(s):  
Finite Volume ◽  
Radiation Energy ◽  
Volume Element ◽  
Diffusion Equations ◽  
Material System ◽  
Two Dimensional ◽  
Adaptation Algorithm ◽  
Radiation Diffusion ◽  
Highly Nonlinear ◽  
Finite Volume Element

AbstractTwo-dimensional three-temperature (2-D 3-T) radiation diffusion equations are widely used to approximately describe the evolution of radiation energy within a multi-material system and explain the exchange of energy among electrons, ions and photons. Their highly nonlinear, strong discontinuous and tightly coupled phenomena always make the numerical solution of such equations extremely challenging. In this paper, we construct two finite volume element schemes both satisfying the discrete conservation property. One of them can well preserve the positivity of analytical solutions, while the other one does not satisfy this property. To fix this defect, two as repair techniques are designed. In addition, as the numerical simulation of 2-D 3-T equations is very time consuming, we also devise a mesh adaptation algorithm to reduce the cost. Numerical results show that these new methods are practical and efficient in solving this kind of problems.

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