Harmonics-Based Inhomogeneous Plane-Wave Method (HIPW)

A formulation is presented for fast interactions between subdomains in two-dimensional (2-D) scattering problems. The formulation combines inhomogeneous plane waves with cylindrical harmonic decompositions of fields radiated by the subdomains. It is shown that the complexity of interactions naturally decays with the distance between subdomains and that very few elementary operations are involved at the lowest level. An example of iterative solution for scattering by a collection of cylinders validates the proposed approach.

[1]  C. Craeye,et al.  Complex patterns devoted to physical compression of MoM matrices , 2013, 2013 7th European Conference on Antennas and Propagation (EuCAP).

[2]  Leslie Greengard,et al.  Remarks on the implementation of wideband FMM for the Helmholtz equation in two dimensions , 2006 .

[3]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[4]  Juan R. Mosig,et al.  A subdomain multilevel approach for the efficient MoM analysis of large planar antennas , 2000 .

[5]  Clive Parini,et al.  Spherical near-field antenna measurements , 2014, Theory and Practice of Modern Antenna Range Measurements, 2nd Expanded Edition, Volume 2.

[6]  V. Rokhlin,et al.  The fast multipole method (FMM) for electromagnetic scattering problems , 1992 .

[7]  Sergej Rjasanow,et al.  Adaptive Low-Rank Approximation of Collocation Matrices , 2003, Computing.

[8]  R. Harrington.  Time-Harmonic Electromagnetic Fields , 1961 .

[9]  Thorkild B. Hansen,et al.  Exact Plane-Wave Expansion With Directional Spectrum: Application to Transmitting and Receiving Antennas , 2014, IEEE Transactions on Antennas and Propagation.

[10]  Weng Cho Chew,et al.  Fast inhomogeneous plane wave algorithm for the fast analysis of two‐dimensional scattering problems , 1999 .

[11]  Jin Au Kong,et al.  Theory of electromagnetic waves , 1975 .

[12]  Germund Dahlquist,et al.  Numerical methods in scientific computing , 2008 .

[13]  Thorkild B. Hansen.  Numerical Properties of a Gaussian Translation Operator for the 2D FMM , 2014, IEEE Transactions on Antennas and Propagation.

[14]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[15]  Raj Mittra,et al.  Macro Basis Function Framework for Solving Maxwell’s Equations in Surface Integral Equation Form , 2014 .

[16]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[17]  F. Gori,et al.  Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach , 1996 .

[18]  E. Martini,et al.  A Domain Decomposition Method Based on a Generalized Scattering Matrix Formalism and a Complex Source Expansion , 2010 .

[19]  Jin-Fa Lee,et al.  A low-rank IE-QR algorithm for matrix compression in volume integral equations , 2004, IEEE Transactions on Magnetics.

[20]  A. Heldring,et al.  On the degrees of freedom in the interaction between sets of elementary scatterers , 2009, 2009 3rd European Conference on Antennas and Propagation.