Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30132
A Comparative Study of High Order Rotated Group Iterative Schemes on Helmholtz Equation

Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

Abstract:

In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1126561

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 755

References:


[1] M.K. Akhir, M. Othman, J. Sulaiman, Z.A. Majid, and M. Suleiman, Numerical solutions of Helmholtz using a new four-point EGMSOR iterative method equations, Appl. Math. Science, Vol. 80, 2011, pp. 3991-4004.
[2] M.K. Akhir, M. Othman, J. Sulaiman, Z.A. Majid, M. Suleiman, Half-sweep iterative method for solving 2D Helmholtz equations, International Journal of Applied Mathematics & Statistics, Vol. 29, No. 5, 2012, pp. 101-109.
[3] M.K. Akhir, M. Othman, Z. Abdul Majid, and M. Suleiman, Four point explicit decoupled group iterative method applied to two-dimensional Helmholtz equation. International Journal of Math. Analysis, vol. 6, no. 20, 2012, pp. 963-974.
[4] N. H. M. Ali and W. P. Teng, New Fourth Order Explicit Group Method in the Solution of the Helmholtz Equation, World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical and Quantum Engineering, Vol. 9 no. 1, 2015, pp. 7-11.
[5] M. Nabavi, M. H. K. Siddiqui, J. Dargahi, A new 9-point sixth order accurate compact finite difference method for the Helmholtz equation, Journal of Sound and Vibration, Vol. 307, 2007, pp. 972-982.
[6] Y. Saad, Iterative Methods for Sparse Linear Systems, second edition, PWS Publishing Company, Boston, 2000.
[7] W. P. Teng and N. H. M. Ali, Higher Order Rotated Iterative Scheme for the 2D Helmholtz Equation, Proceedings of the 21st National Symposium on Mathematical Sciences (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability, AIP Proceedings Volume 1605, 2014, pp. 155-160.
[8] Wang, and J. Zhang, “Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D Poisson equation”, Journal of Computation Physics, 228, 2009, pp. 137-146.