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The efficient solution of arbitrary 2-D scattering problems by the cylindrical method of lines

In this paper, a novel cylindrical method of lines (MoL) is proposed to compute the unbounded 2-D scattering problems. In this approach, by discretizing the angular direction with radial lines, the 2-D Laplacian equation is reduced to a series of 1-D differential equations, which can be solved analytically in the radial direction. The computational cost is reduced significantly because discretization is only applied on the angular direction, and the accuracy of the solution is improved greatly because of the semi-analytical nature of the MoL and the elimination of an artificial boundary condition. Theoretical analysis and numerical experiments show that the cylindrical MoL is applicable to arbitrarily shaped scatterer with lossless or lossy dielectric media.