Derivation of Green’s Function for the Interior Region of a Closed Cylinder

Document Type : Research Article


1 BSc. Student, Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

2 Assistant Professor, Department of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, Iran


The importance of constructing the appropriate Green function to solve a wide range of problems inelectromagnetics and partial differential equations is well-recognized by those dealing with classical electrodynamics and related fields. Although the subject of obtaining the Green function for certain geometries has been extensively studied and addressed in numerous sources, in this paper a systematic method using the Method of Separation of Variables has been employed to scrutinize the Green function with Dirichlet boundary condition for the interior region of a closed cylinder. With further rigorous elaboration, we have demonstrated clearly the path through which the Green function can be accomplished. Additional verifications both in analytical and computer-simulating problems have also been performed to demonstrate the validity of our analysis.


Jackson, J.D., “Classical Electrodynamics”, 3rd ed., New York, Wiley, 1999.
Morse P.M., Feshbach H., “Methods of Theoretical Physics”, McGraw-Hill, 1953.
Barton G., “Elements of Green’s functions and propagation: potentials, diffusion, and waves”, Oxford University Press, 1989.
Balanis C.A., “Green’s Functions” in Advanced Engineering Electromagnetics, 2nd ed., Wiley, 2012.
Conway J.T., Cohl S. H., “Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function”, Journal of Applied Mathematics and Physics, 66, 2009.
Sun J., et al., “Rigorous Green's function formulation for transmembrane potential induced along a 3-D infinite cylindrical cell”, Antennas and Propagation Society International Symposium IEEE, 4: pp. 4076-4079, 2004.
Wu J., Wang C., “An Efficient Method for Intensive Computations of Cylindrical Green's Functions”, Antennas and Propagation Society International Symposium (APSURSI), pp. 2032-2033, 2014
Wu J., Wang C., “Efficient Modeling of Antennas Conformal to Cylindrical Medium Using Cylindrical Green’s Function”, International Symposium on Antennas and Propagation and North American Radio Science Meeting, 2015.
A.Ye. Svezhentsev et al.,” Green’s Functions for Probe-Fed Arbitrary-Shaped Cylindrical Microstrip Antennas”, Antennas and Propagation, IEEE Transaction on, 63: pp. 993-1003, 2015.
Myint-U T., Debnath L., “Linear Partial Differential Equations for Scientists and Engineers”, 4th ed., Birkhauser, 2007.
Arfken G.B., Weber H.J., Harris F.E., “Mathematical Methods for Physicists, A Comprehensive Guide”, 7th ed., Academic Press, 2013.
Abramowitz M., Stegun I.A., “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables”, Dover Publications, 1972