## Multilevel Green’s function interpolation method for analysis of 3-D frequency selective structures using volume/surface integral equation

JOSA A, Vol. 27, Issue 2, pp. 308-318 (2010)

http://dx.doi.org/10.1364/JOSAA.27.000308

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### Abstract

In this paper, we present the multilevel Green’s function interpolation method (MLGFIM) for analyses of three-dimensional doubly periodic structures consisting of dielectric media and conducting objects. The volume integral equation (VIE) and surface integral equation (SIE) are adopted, respectively, for the inhomogeneous dielectric and conducting objects in a unit cell. Conformal basis functions defined on curvilinear hexahedron and quadrilateral elements are used to solve the volume/surface integral equation (VSIE). Periodic boundary conditions are introduced at the boundaries of the unit cell. Computation of the space-domain Green’s function is accelerated by means of Ewald’s transformation. A periodic octary-cube-tree scheme is developed to allow adaptation of the MLGFIM for analyses of doubly periodic structures. The proposed algorithm is first validated by comparison with published data in the open literature. More complex periodic structures, such as dielectric coated conducting shells, folded dielectric structures, photonic bandgap structures, and split ring resonators (SRRs), are then simulated to illustrate that the MLGFIM has a computational complexity of

© 2010 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(000.3870) General : Mathematics

(000.4430) General : Numerical approximation and analysis

(350.7420) Other areas of optics : Waves

**ToC Category:**

Mathematical methods in physics

**History**

Original Manuscript: September 18, 2009

Revised Manuscript: December 19, 2009

Manuscript Accepted: December 19, 2009

Published: January 25, 2010

**Citation**

Yan Shi and Chi Hou Chan, "Multilevel Green's function interpolation method for analysis of 3-D frequency selective structures using volume/surface integral equation," J. Opt. Soc. Am. A **27**, 308-318 (2010)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-2-308

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