A procedure for generating curved meshes, suitable for high-order finite element analysis, is described. The strategy adopted is based upon curving a generated initial mesh with planar edges and faces by using a linear elasticity analogy. The analogy employs boundary loads that ensure that nodes representing curved boundaries lie on the true surface. Several examples, in both two and three dimensions, illustrate the performance of the proposed approach, with the quality of the generated meshes being analysed in terms of a distortion measure. The examples chosen involve geometries of particular interest to the computational fluid dynamics community, including anisotropic meshes for complex three dimensional configurations.

SUMMARYThe Yee algorithm is a highly efficient time domain co-volume method for computational electromagnetics using a pair of staggered orthogonal cartesian meshes. An equivalent unstructured mesh process is readily implemented on a primal Delaunay tetrahedral mesh and its orthogonal Voronoï dual. The difficulty, for practical applications, is ensuring that both the Delaunay and the Voronoï meshes possess the necessary properties to enable an accurate and efficient solution to be obtained by this approach. This is a mesh generation problem and it is addressed here by using a combination of a point distribution provided by an ideal tetrahedral mesh, a constrained centroidal Voronoï tessellation method and a mesh quality optimization procedure. For the selected application area of electromagnetic wave scattering problems, the computational efficiency is enhanced by using a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of the scatterer and hexahedral elements elsewhere. Three examples are included to demonstrate the viability of the proposed approach and to indicate the numerical performance that can be achieved.

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SUMMARYThe numerical solution of Maxwell's curl equations in the time domain is achieved by combining an unstructured mesh finite element algorithm with a cartesian finite difference method. The practical problem area selected to illustrate the application of the approach is the simulation of three-dimensional electromagnetic wave scattering. The scattering obstacle and the free space region immediately adjacent to it are discretized using an unstructured mesh of linear tetrahedral elements. The remainder of the computational domain is filled with a regular cartesian mesh. These two meshes are overlapped to create a hybrid mesh for the numerical solution. On the cartesian mesh, an explicit finite difference method is adopted and an implicit/explicit finite element formulation is employed on the unstructured mesh. This approach ensures that computational efficiency is maintained if, for any reason, the generated unstructured mesh contains elements of a size much smaller than that required for accurate wave propagation. A perfectly matched layer is added at the artificial far field boundary, created by the truncation of the physical domain prior to the numerical solution. The complete solution approach is parallelized, to enable large-scale simulations to be effectively performed. Examples are included to demonstrate the numerical performance that can be achieved.

This paper describes the development of modelling techniques and simulation tools for the electromagnetic analysis of aircraft. It is shown that hybrid solvers and multi-scale techniques can be used effectively to analyse the electromagnetic response of aircraft. The importance of supplementing models with appropriate measurement and characterization techniques for parameter extraction and for validation is also demonstrated.