**Author details**

solution produced by the two-corner scatterer. The difference between the actual solution and that produced by rounding is measured using the *L*<sup>2</sup> norm (83) and *L*<sup>∞</sup> norm (84).

The tests were run for all three boundary conditions for *ka* = 1, 5, 10, and 2*π*, and radii of curvature *ρ* = 0.05, 0.04, ..., 0.01 and, in the case of the impedance loaded scatterers, a number of impedance parameters. The results were similar for all wave numbers and Table 8 presents the results for *ka* = 2*π*. The smaller the radius of curvature used for the rounding, the smaller the measured error. Both the absolute and relative errors were measured. The relative error is expressed as percentage of the same norm of the far-field of the two-corner

Using a radius of curvature of *ρ* = 0.02 , using the *L*<sup>2</sup> norm produces an error of 3.8% in the Dirichlet case, 1.6% in the Neumann case and 2.4% for the impedance boundary condition. Similarly, the *L*<sup>∞</sup> norm measures an error of 2.4% in the Dirichlet case, 1.5% in the Neumann case and 1.4% for the impedance boundary condition. Using a radius of curvature of *ρ* = 0.01, using the *L*<sup>2</sup> norm produces an error of 1.2% in the Dirichlet case, 0.4% in the Neumann case and 1% for the impedance boundary condition. Similarly, the *L*<sup>∞</sup> norm measures an error of 0.9% in the Dirichlet case, 0.4% in the Neumann case and 0.6% for the

> **Comparison of rounding effect to actual two-corner scatterer** ρ *L*<sup>2</sup> **Norm** % **Difference** *L*<sup>∞</sup> **Norm** % **Difference**

0.05 0.0219 10 0.1052 7.5 0.04 0.0164 7.7 0.0792 5.6 0.03 0.0112 5.3 0.0543 3.9 0.02 0.0068 3.8 0.0332 2.4 0.01 0.0026 1.2 0.0128 0.9

0.05 0.0094 7 0.0433 6.6 0.04 0.0065 4.9 0.0300 4.6 0.03 0.0040 3.0 0.0184 2.8 0.02 0.0021 1.6 0.0097 1.5 0.01 0.0006 0.4 0.0027 0.4

0.05 0.0113 6.9 0.0487 4.0 0.04 0.0086 5.3 0.0374 3.1 0.03 0.0061 3.7 0.0264 2.1 0.02 0.0039 2.4 0.0167 1.4 0.01 0.0017 1.0 0.0074 0.6

In this paper we have described numerical schemes and their implementation for the solution of scattering of a plane wave by two different cylindrical structures: a single-cornered structure and a second structure with two corners, each with three different boundary conditions imposed on their surfaces - soft, hard and an impedance boundary condition. We

scatterer.

26 Advanced Electromagnetic Waves

impedance boundary condition.

**Dirichlet**

**Neumann**

**Impedance** *λ* = 1 + *i*

**Table 8.** Direction of incident plane wave *θ*<sup>0</sup> = 0 with *ka* = 2*π*.

**6. Conclusion**

Paul D. Smith∗ and Audrey J. Markowskei

\*Address all correspodence to: paul.smith@mq.edu.au

Department of Mathematics, Macquarie University, Sydney, Australia
