Vol. 48
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2013-01-26
Convex Meshfree Solutions for Arbitrary Waveguide Analysis in Electromagnetic Problems
By
Progress In Electromagnetics Research B, Vol. 48, 131-149, 2013
Abstract
This paper presents a convex meshfree framework for solving the scalar Helmholtz equation in the waveguide analysis of electromagnetic problems. The generalized meshfree approximation (GMF) method using inverse tangent basis functions and cubic spline weight functions is employed to construct the first-order convex approximation which exhibits a weak Kronecker-delta property at the waveguide boundary and allows a direct enforcement of homogenous Dirichlet boundary conditions for the transverse magnetic (TM) mode analyses. Three arbitrary waveguide examples are analyzed to demonstrate the accuracy of the presented formulation, and comparison is made by the analytical, finite element and meshfree solutions.
Citation
Li-Fang Wang, "Convex Meshfree Solutions for Arbitrary Waveguide Analysis in Electromagnetic Problems," Progress In Electromagnetics Research B, Vol. 48, 131-149, 2013.
doi:10.2528/PIERB12122110
References

1. Ihlenburg, F. and I. Babuska, "Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of FEM," Comp. Math. Appl., Vol. 30, No. 9, 9-37, 1995.
doi:10.1016/0898-1221(95)00144-N

2. Harari, I. and T. J. R. Hughes, "Finite element method for the Helmholtz equation in an exterior domain: Model problems," Comp. Meth. Appl. Mech. Eng., Vol. 87, 59-96, 1991.
doi:10.1016/0045-7825(91)90146-W

3. Harari, I. and T. J. R. Hughes, "Galerkin/least squares finite element method for the reduced wave equation with non-reflecting boundary conditions," Comp. Meth. Appl. Mech. Eng., Vol. 92, 441-454, 1992.

4. Babuska, I., F. Ihlenburg, E. Paik, and S. Sauter, "A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution," Comp. Meth. Appl. Mech. Eng., Vol. 128, 325-359, 1995.
doi:10.1016/0045-7825(95)00890-X

5. Farhat, C., I. Harari, and L. P. Franca, "The discontinuous enrichment method," Comp. Meth. Appl. Mech. Eng., Vol. 190, 6455-6479, 2001.
doi:10.1016/S0045-7825(01)00232-8

6. Zienkiewicz, O. C., "Achievements and some unsolved problems of the finite element method," Int. J. Numer. Meth. Engrg., Vol. 47, 9-28, 2000.
doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P

7. Ooi, B. L. and G. Zhao, "Element-free method for the analysis of partially-filled dielectric waveguides," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 2, 189-198, 2007.
doi:10.1163/156939307779378772

8. Miao, Y., Y. Wang, and H. Wang, "A meshless hybrid boundary-node method for Helmholtz problems," Eng. Anal. Boundary Elem, Vol. 33, 120-127, 2009.
doi:10.1016/j.enganabound.2008.05.009

9. Correa, B. C., E. J. Silva, A. R. Fonseca, D. B. Oliveria, and R. C. Mesquita, "Meshless local Petrov-Galerkin in solving microwave guide problems," IEEE Trans. Magnetics, Vol. 47, 1526-1529, 2011.
doi:10.1109/TMAG.2010.2091496

10. Belytschko, T., Y. Y. Lu, and L. Gu, "Element-free Galerkin methods," Int. J. Numer. Meth. Engrg., Vol. 37, 229-256, 1994.
doi:10.1002/nme.1620370205

11. Liu, W. K., S. Jun, and Y. F. Zhan, "Reproducing kernel particle methods," Int. J. Numer. Meth. Fluids, Vol. 20, 1081-1106, 1995.
doi:10.1002/fld.1650200824

12. Kansa, E. J., "Multiqudrics --- A scattered data approximation scheme with applications to computational fluid-dynamics --- I: Surface approximations and partial derivatives," Comp. Math. Appl., Vol. 9, 127-145, 1992.

13. Jiang, P. L., S. Q. Li, and C. H. Chan, "Analysis of elliptic waveguides by a meshless collocation method with the Wendland adial basis functions," Microwave and Optical Technology Letters, Vol. 32, No. 2, 162-165, 2002.
doi:10.1002/mop.10119

14. Lai, S. J., B. Z. Wang, and Y. Duan, "Solving Helmholtz equation by meshless radial basis functions method," Progress In Electromagnetics Research B, Vol. 24, 351-367, 2010.
doi:10.2528/PIERB10062303

15. Kaufmann, T., Y. Yu, C. Engstrom, Z. Chen, and C. Fumeaux, "Recent developments of meshless radial point interpolation method for time-domain electromagnetics," Int. J. Numer. Model: Elect. Networks, Devices and Fields, Vol. 25, 468-489, 2012.
doi:10.1002/jnm.1830

16. Wu, C. T., C. K. Park, and J. S. Chen, "A generalized meshfree approximation for the meshfree analysis of solids," Int. J. Numer. Meth. Engrg., Vol. 85, 693-722, 2011.
doi:10.1002/nme.2991

17. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 90, 2nd Ed., Cambridge University Press, New York, 1996.

18. Harrington, R. F., Time-harmonic Electromagnetic Fields, Wiley-IEEE Press, New York, 2001.
doi:10.1109/9780470546710

19. Marcuvitz, N., Waveguide Handbook, Peter Peregrinus Ltd., London, 1993.

20. Shaw, A. and D. Roy, "NURBS-based parametric mesh-free methods," Comput. Methods Appl. Mech. Engrg., Vol. 197, 1541-1567, 2008.
doi:10.1016/j.cma.2007.11.024