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Implementation and Experiments of Sparse Matrix Data Structure for Heat Conduction Equations
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 Title & Authors
Implementation and Experiments of Sparse Matrix Data Structure for Heat Conduction Equations
Kim, Jae-Gu; Lee, Ju-Hee; Park, Geun-Duk;
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 Abstract
The heat conduction equation, a type of a Poisson equation which can be applied in various areas of engineering is calculating its value with the iteration method in general. The equation which had difference discretization of the heat conduction equation is the simultaneous equation, and each line has the characteristic of expressing in sparse matrix of the equivalent number of none-zero elements with neighboring grids. In this paper, we propose a data structure for sparse matrix that can calculate the value faster with less memory use calculate the heat conduction equation. To verify whether the proposed data structure efficiently calculates the value compared to the other sparse matrix representations, we apply the representative iteration method, CG (Conjugate Gradient), and presents experiment results of time consumed to get values, calculation time of each step and relevant time consumption ratio, and memory usage amount. The results of this experiment could be used to estimate main elements of calculating the value of the general heat conduction equation, such as time consumed, the memory usage amount.
 Keywords
Sparse Matrix;Data Structure;Heat Conduction Equation;Conjugate Gradient Methods;
 Language
Korean
 Cited by
 References
1.
Thompson, Joe F.; Warsi, Zahir UA; Mastin, C. Wayne. Numerical grid generation: foundations and applications. Amsterdam: North-holland, 1985.

2.
Im, Eun-Jin. "An Efficient Computation of Matrix Triple Products." Journal of the Korea Society of Computer and Information 2006, Nov.: 141-149.

3.
Myong, H. K. Evaluation of Numerical Approximations of Convection Flux in Unstructured Cell-Centered Method. Journal of computational fluids engineering, 2006, Jan.: 36-42.

4.
Boo, Hee-Hyung; Kim, Sung-Ho. Two dimensional variable-length vector storage format for efficient storage of sparse matrix in the finite element method. Journal of the Korea Society of Computer and Information, 2012, Sep.: 9-16.

5.
White, Frank M. Fluid mechanics.(7thedn). 2011.

6.
Golub, Gene H.; Van Loan, Charles F. Matrix computations. JHU Press, 2012.

7.
Conjugate gradient method Wiki, https://en.wikipedia.org/wiki/Conjugate_gradient_method

8.
Sparse matrix Wiki, https://en.wikipedia.org/wiki/Sparse_matrix

9.
Liu, Chao, Junmin Ye, and Yining Ma. "Storage and Solving of Large Sparse Matrix Linear Equations." 2012 Fourth International Conference on Computational and Information Sciences. IEEE, 2012.