Paper Info
Title
Modified Incomplete Cholesky Preconditioned Conjugate Gradient Algorithm on GPU for the 3D Parabolic Equation.
Abstract
In this study, for solving the three-dimensional partial differential equation u(t) = u(xx) + u(yy) + u(zz), an efficient parallel method based on the modified incomplete Cholesky preconditioned conjugate gradient algorithm (MICPCGA) on the GPU is presented. In our proposed method, for this case, we overcome the drawbacks that the MIC pre-conditioner is generally difficult to be parallelized on the GPU due to the forward/backward substitutions, and thus present an efficient parallel implementation method on the GPU. Moreover, a vector kernel for the sparse matrix-vector multiplication, and optimization of vector operations by grouping several vector operations into a single kernel are adopted. Numerical results show that our proposed forward/backward substitutions and MICPCGA on the GPU both can achieve a significant speedup, and compared to an approximate inverse SSOR pre-conditioned conjugate gradient algorithm (SSORPCGA), our proposed MICPCGA obtains a bigger speedup, and outperforms it in solving the three-dimensional partial differential equation.
Year
DOI
Venue
2013
10.1007/978-3-642-40820-5_25
Lecture Notes in Computer Science
Keywords
Field
DocType
conjugate gradient algorithm,modified incomplete Cholesky preconditioner,parabolic equation,GPU
Kernel (linear algebra),Conjugate gradient method,Preconditioner,Computer science,Incomplete Cholesky factorization,Minimum degree algorithm,Algorithm,Partial differential equation,Cholesky decomposition,Speedup
Conference
Volume
Issue
ISSN
8147
null
0302-9743
Citations 
PageRank 
References 
0
0.34
4
Authors
3
Name
Order
Citations
PageRank
Jiaquan Gao1697.62
Bo Li288.65
HE Gui-xia3315.97