**Commenced**in January 2007

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**Edition:**International

**Paper Count:**31830

##### Parallel Explicit Group Domain Decomposition Methods for the Telegraph Equation

**Authors:**
Kew Lee Ming,
Norhashidah Hj. Mohd. Ali

**Abstract:**

**Keywords:**
Telegraph equation,
explicit group iterative scheme,
domain decomposition algorithm,
parallelization.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1063060

**References:**

[1] Kew, L.M. and Ali, N.H.M. "Explicit Group Iterative Methods for the Solution of Telegraph Equations", Lecture Notes In Engineering and Computer Science, World Congress On Engineering 2010, The 2010 International Conference of Applied and Engineering Mathematics, 30th June - 2nd July 2010, Imperial College, London, 2010, pp.1770- 1775.

[2] Saad, Y. "Iterative Methods for Sparse Linear Systems". 2nd Edition. pp. 382-421.

[3] Abdullah, A.R. "The Four Point Explicit Decoupled Group EDG Method: A Fast Poisson Solver". International Journal of Computer Mathematics, 38, 1991, pp.61-70.

[4] Yousif, W.S. and Evans, D.J. "Explicit De-Coupled Group Iterative Methods and Their Parallel Implementations". Parallel Algorithms and Applications, 7, 1995, pp.53-71.

[5] Evans, D.J. "Group Explicit Methods for the Numerical Solution of Partial Differential Equations". Loughborough University of Technology, UK, Gordon and Breach Science Publisher, The Netherlands, 1997, pp.106-162.

[6] Dryja, M. and Widlund, O.B. "Some Domain Decomposition Algorithms for Elliptic Problems", in: L. Hayes, D. Kincaid (Eds.), Iterative Methods for Large Linear Systems, Academic Press, San Diego, CA. 1989.

[7] Cai, X.-C. and Widlund, O.B. "Domain Decomposition Algorithms for Indefinite Elliptic Problems", SIAM J. Sci. Statist. Comput., 13, 1992, pp. 243-258.

[8] Dawson, C.N., Du, Q., and Dupont, T.F. "A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation". Mathematics of Computation, 57(195), 1991, pp. 63-71.

[9] Jun, Y. and Mai, T.Z. (2006). "IPIC Domain Decomposition Algorithm for Parabolic Problems". Applied Mathematics and Computation, 177, 2006, pp. 352-364.

[10] Ali, A. "Introduction to Hybrid MPI/OpenMP Programming". Presented at ICTP Advanced School in High Performance and Grid Computing, 11-22 April 2011, Abdus Salam ICTP - Trieste.

[11] Dehghan, M. and Shokri, A., "A Meshless Method for Numerical Solution of a Linear Hyperbolic Equation with Variable Coefficients in Two Space Dimensions." Numerical Methods for Partial Differential Equations, 2008, pp.494-506.