


Materials of this type are frequency dependent and have an additional parameter, the chirality, which couples the electric to the magnetic field, making the simulation even more challenging. 12– 13, we consider a further extension that allows for the modelling of bi-isotropic materials. This allows us to consider the simulation of problems involving crystals, or composite materials, where the orientation of fibres plays an important role. 9– 11, we move on to consider anisotropic lossy materials, where the material parameters, electric permittivity \(\varepsilon\), the magnetic permeability \(\mu\) and the electric and magnetic conductivites \(\sigma ,\sigma _m\), become second order tensors. The calculation of the RCS distribution of a more complex PEC aircraft geometry and the simulation of transmission of an electromagnetic pulse through a radome are presented in Sect.

7, we validate our algorithm by comparing the numerical and analytical solutions for the RCS distribution for problems involving, dielectric lossy and coated spheres of different electrical lengths. Section 6 describes the method adopted for the calculation of the distribution of the radar cross section (RCS). The treatment of the different kinds of boundary conditions is discussed in Sect. Section 4 is devoted to the mesh generation process, which is one of the most crucial parts for the successful implementation of the proposed scheme. Section 3 introduces the FDTD method and illustrates the discretisation of the Maxwell equations on both a structured and an unstructured mesh. 2, we outline the problem of interest and employ a scattered field formulation for Maxwells equation in integral form for problems involving an isotropic lossy dielectric material and/or a perfect electric conductor (PEC). This paper is structured as follows: In Sect. The proposed implementation is edge and face based, which means that it is not restricted to specific mesh element types and can handle any form of polyhedron. With this method, hybrid meshes can be naturally incorporated, without requiring the inter-mesh interpolation, and consequent non-physical diffraction effects mesh interfaces, that plagues many hybrid approaches. An alternative approach to generalising the FDTD algorithm to unstructured meshes is to employ a primal unstructured Delaunay mesh and its orthogonal Voronoi dual graph . Unfortunately, these methods do not retain the efficiency of the original scheme . To retain these benefits, for simulations involving geometries of complex shape, non-uniform and unstructured mesh FDTD implementations have been suggested, such as the generalised Yee algorithm and the Yee-like algorithm.
#Fdtd free
In addition, the scheme preserves the energy and amplitude of waves, is divergence free and can readily be parallelised. The algorithm has the additional advantages of simplicity, low computational cost and, as no linear algebra is required, there is no inherent limit to the size of the simulation.

The use of staggered meshes enables the interleaving of the unknown nodal values of the electric and magnetic field components, resulting in an explicit algorithm that is second order accurate in both space and time. In its standard form, the FDTD algorithm is implemented on structured staggered spatial meshes. In this paper, we consider the simulation of problems in electromagnetics using unstructured co-volume staggered meshes and a generalisation of the Yee finite difference time domain (FDTD) method . The power of the proposed solution approach is demonstrated by considering a range of scattering and/or transmission problems involving perfect electric conductors and isotropic lossy, anisotropic lossy and isotropic frequency dependent chiral materials. Difficulties associated with ensuring the necessary quality of the generated meshes will be discussed. Computational efficiency is improved by employing a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of curved interfaces and hexahedral elements elsewhere. This co-volume method is based upon the use of a Delaunay primal mesh and its high quality Voronoi dual. For the solution of such problems, we generalise the approach and adopt an unstructured mesh FDTD method. However, accuracy losses result when it is used for modelling electromagnetic interactions with objects of arbitrary shape, because of the staircased representation of curved interfaces. The standard method uses a pair of staggered orthogonal cartesian meshes. The Yee finite difference time domain (FDTD) algorithm is widely used in computational electromagnetics because of its simplicity, low computational costs and divergence free nature.
