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This paper presents a curvilinearly‐established finite‐difference time‐domain methodology for the enhanced 3D analysis of electromagnetic and acoustic propagation in generalised electromagnetic compatibility devices, junctions or bent ducts. Based on an exact multimodal decomposition and a higher‐order differencing topology, the new technique successfully treats complex systems of varying cross‐section and guarantees the consistent evaluation of their scattering parameters or resonance frequencies. To subdue the non‐separable modes at the structures' interfaces, a convergent grid approach is developed, while the tough case of abrupt excitations is also studied. Thus, the proposed algorithm attains significant accuracy and savings, as numerically verified by various practical problems.

A systematic, non‐orthogonal FDTD algorithm for the unified and fully dual construction of curvilinear PMLs in 3‐D lossy electromagnetic and advective acoustic problems, is presented in this paper. Postulating a consistent mathematical formulation, the novel methodology introduces a set of general vector parametric equations that describe wave propagation in both media and facilitate the effective treatment of the remarkably complex, arbitrarily‐aligned (non‐uniform) source or mean flow terms, particularly at low frequencies. The discretization procedure is performed via accurate higher‐order FDTD topological concepts, which along with a well‐posed variable transformation, suppress the undesired lattice dispersion and anisotropy errors. Hence, due to these additional degrees of design freedom and their optimal establishment, the new stable PMLs (split‐field or Maxwellian) accomplish a critical attenuation of the evanescent, vorticity or elastic wave families by carefully accounting for every loss mechanism. Numerical investigation reveals the superiority of the proposed technique in terms of various open‐region, waveguide and ducted‐domain simulations.