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B 2-Spline Interpolation Technique for Overset Grid Generation and Finite-Difference Time-Domain Method

By Bong Siaw Wee, Shafrida Sahrani, and Kismet Anak Hong Ping
Progress In Electromagnetics Research C, Vol. 86, 177-190, 2018


In this paper, B2-spline interpolation technique for Overset Grid Generation (OGG) and Finite-Difference Time-Domain (FDTD) method is developed. B2-spline or biquadratic spline interpolation offers better accuracy compared to the bilinear interpolation. The two-dimensional (2-D) numerical simulations are carried out for electromagnetic (EM) field analysis to measure the scattered fields for an unknown object in a free space and a dielectric medium. There are 2 antennas utilized in this work, each antenna will become transmitter sequentially to transmit a microwave pulses while another acts as receiver to collect the scattered fields in the OGG-FDTD lattice. In order to analyse the efficiency of proposed method, the scattered fields that collected by receiver antenna will be investigated with relative error. The results show that OGG-FDTD method with B2-spline interpolation gives lower relative error than bilinear interpolation with 0.0009% differences in a free space and 0.0033% differences in a dielectric medium. Hence, it proves that OGG-FDTD method with B2-spline interpolation has ability to measure the scattered fields around the unknown object efficiently. For future work, the proposed method can be applied to inverse scattering for detection and reconstruction of the buried objects with arbitrary shapes in a complex media.


Bong Siaw Wee, Shafrida Sahrani, and Kismet Anak Hong Ping, "B 2-Spline Interpolation Technique for Overset Grid Generation and Finite-Difference Time-Domain Method," Progress In Electromagnetics Research C, Vol. 86, 177-190, 2018.


    1. Mahajan, S. H. and V. K. Harpale, "Adaptive and non-adaptive image interpolation techniques," International Conference on Computing Communication Control and Automation (ICCUBEA), IEEE, 772-775, 2015.

    2. Sinha, A., M. Kumar, A. K. Jaiswal, and R. Saxena, "Performance analysis of high resolution images using interpolation techniques in multimedia communication system," Signal & Image Processing, Vol. 5, No. 2, 39, 2014.

    3. Gupta, R. B., B. G. Lee, and J. J. Lee, "A new image interpolation technique using exponential B-spline,", 2007.

    4. Singh, M. R. and A. S. Bhide, "A review of image retrieval using different types of interpolation techniques," International Research Journal of Engineering and Technology (IRJET), Vol. 3, No. 12, 1423-1426, 2016.

    5. Moler, C. B., Numerical Computing with MATLAB2004, Society for Industrial and Applied Mathematics, 2004.

    6. Szabados, J. and P. Vértesi, Interpolation of Functions, World Scientific, 1990.

    7. Acharya, T. and A. K. Ray, Image Processing: Principles and Applications, John Wiley & Sons, 2005.

    8. Lehmann, T. M., C. Gonner, and K. Spitzer, "Survey: Interpolation methods in medical image processing," IEEE Transactions on Medical Imaging, Vol. 18, No. 11, 1049-1075, 1999.

    9. Jiang, N. and J. Wang, "Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio," Quantum Information Processing, Vol. 14, No. 11, 4001-4026, 2015.

    10. Warbhe, S. and J. Gomes, "Interpolation technique using non-linear partial differential equation with edge directed bicubic," International Journal of Image Processing (IJIP), Vol. 10, No. 4, 205, 2016.

    11. Iwamatsu, H., R. Fukumoto, M. Ishihara, and M. Kuroda, "Comparative study of over set grid generation method and body fitted grid generation method with moving boundaries," Antennas and Propagation Society International Symposium, AP-S 2008. IEEE, 1-4, 2008.

    12. Spath, H., Two Dimensional Spline Interpolation Algorithms, 1-68, United States of America: A K Peters, Wellesley, Massachusetts, 1995.

    13. Han, D. Y., "Comparison of commonly used image interpolation methods," Proceedings of the 2nd International Conference on Computer Science and Electronics Engineerings (ICCSEE), 1556-1559, 2013.

    14. Xia, P., T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, "Performance comparison of bilinear interpolation, bicubic interpolation, and B-spline interpolation in parallel phase-shifting digital holography," Optical Review, Vol. 20, No. 2, 193-197, 2013.

    15. Sinha, A., "Study of interpolation techniques in multimedia communication system-a review,", 2015.

    16. Azman, A., S. Sahrani, K. H. Ping, and D. A. A. Mat, "A new approach for solving inverse scattering problems with overset grid generation method," TELKOMNIKA (Telecommunication Computing Electronics and Control), Vol. 15, No. 1, 820-828, 2017.

    17. Kaur, K., I. Kaur, and J. Kaur, "Survey on image interpolation," International Journal of Advanced Research in Computer Science and Software Engineering, Vol. 6, No. 5, 613-616, 2016.

    18. Patel, V. and K. Mistree, "A review on different image interpolation techniques for image enhancement," International Journal of Emerging Technology and Advanced Engineering (IJETAE), Vol. 3, 129-133, 2013.

    19. Boor, C. D., A Practical Guide to Spline, Springer-Verlag, 1978.

    20. Schumaker, L. L., Spline Functions: Computational Methods, Society for industrial and applied mathematics (SIAM), 2015.

    21. Thompson, J. F., Z. U. Warsi, and C. W. Mastin, Numerical Grid Generation: Foundations and Applications, 45, North-holland Amsterdam, 1985.

    22. Thompson, J. F., B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation, CRC Press, 1998.

    23. Castillon, L. and G. Legras, "Overset Grid Method for simulation of compressors with nonaxisymmetric casing treatment," Journal of Propulsion and Power, Vol. 29, No. 2, 460-465, 2013.

    24. Renaud, T., A. L. Pape, and S. Péron, "Numerical analysis of hub and fuselage drag breakdown of a helicopter configuration," CEAS Aeronautical Journal, Vol. 4, No. 4, 409-419, 2013.

    25. Castillon, L., G. Billonnet, J. Riou, S. Péron, and C. Benoit, "A technological effect modeling on complex turbomachinery applications with an overset grid numerical method," Journal of Turbomachinery, Vol. 136, No. 10, 101005, 2014.

    26. Wiart, L., O. Atinault, D. Hue, R. Grenon, and B. Paluch, "Development of NOVA aircraft configurations for large engine integration studies," 33rd AIAA Applied Aerodynamics Conference, 2015.

    27. Courant, R., K. Friedrichs, and H. Lewy, "On the partial difference equations op mathematical physics," Mathematische Annalen, Vol. 100, No. 1, 32-74, 1928.