What is it about?
The PML developed is demonstrated through a mapping of the TLM shunt node to a domain with spatial coordinates stretched to a complex domain. In the proposed formulation, the PML layer is to be interpreted as a network of transmission lines whose constitutive RLC components have been transformed by a complex stretch factor. This formulation offers a unified algorithm and is particularly advantageous as the results obtained show a capability for effectively terminating both lossy and lossless dielectric media. Owing to its simplicity, extensions to other TLM nodes, such as the 2D series node and the widely used three-dimensional symmetrical condensed node, are implicitly implied.
Photo by Linus Mimietz on Unsplash
Why is it important?
The PML is widely accepted as the superior absorbing boundary technique and has become a prevalent feature in electromagnetic simulation packages. However, the challenge of developing an efficient and numerically stable TLM-PML formulation is also very well identified amongst TLM researchers. Hence, only a handful of implementations have been reported to date. In light of the huge benefits attainable, we implement, for the first time, a stretched coordinate PML suitable for terminating 2D TLM grids.
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This page is a summary of: Stretched-Coordinate PML in 2D TLM Simulations, IET Science Measurement & Technology, December 2019, the Institution of Engineering and Technology (the IET), DOI: 10.1049/iet-smt.2019.0340.
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Electric field intensity in Naca0015 airfoil
For further illustrative purposes the mapped PML is applied to a topical wave-structure application, involving the plane wave scattering of a PEC airfoil with profile Naca0015 . The airfoil structure was placed in a 0.6 m × 2 m computational domain which was uniformly meshed with ∆l = 5 mm. The plane wave was incident on the airfoil along the x direction. The electric field intensity (in dB) at time t = 30 ns in simulations where a 20 layer PML and matched boundary termination were applied is shown in Figs. 7a and b, respectively. The high absorbing capability of the PML is clearly demonstrated by how quickly the overall energy is attenuated in Fig. 7b compared to Fig. 7a where the matched boundary is employed. Finally, it should be reported that numerical instability has not been observed in any of the investigations carried out in this work; therefore, further demonstrating the utility of the proposed formulation.
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