This dissertation work investigates the numerical method for solving EMC problems involving electrically large and complex platform. Numerical simulation of the antenna couplings on the aircraft is of great interest in EMC community. Conventional CEM solvers suffer inefficiency and inflexibility in modelling this kind of problems. One of the challenges comes from the multi-scale physics in the geometry containing both electrically large platform and antennas with electrically small structures. Also, using conventional CEM solvers, the user may have the dilemma of choosing between the PDE based methods , like FEM, which are convenient and accurate in modelling complex materials but requires volume mesh, and IE based methods, which only require surface discretization but are not convenient in modelling antennas with complex materials.
In this dissertation, a MSDDM has been proposed to model the problems with electrically large and complex structures. Using MSDDM, the problem of antenna coupling can be decomposed into antenna sub-domains and platform sub-domains, for which different CEM solvers can be applied. This gives an efficient way to precondition the global system. It hybridizes the strength of PDE based methods and IE methods. Also, the CEM solvers in MSDDM can be stored in out-of-core memory, which enables it to solve large problem within limited memory.
MSDDM is applied to solve the EMC problem on a mock-up aircraft platform. It has been recognized that the decomposition scheme for MSDDM is inflexible in modelling electrically large objects, which need to be decomposed into smaller blocks for memory reason. In most cases, it will be the platform who has the highest memory cost. With MSDDM, the user needs to decompose the geometry and re-mesh it, which is undesirable. A new non-overlapping IEDDM has been proposed in this dissertation to solve this issue. IEDDM can decompose the surface of PEC into non-overlapping sub-domains. Hence in dealing with the electrically large object, the user can obtain the mesh by decompose the original surface mesh into open partitions and analytically refine each of them. This decomposition can be easily implemented in an automatic fashion.
With MSDDM and IEDDM, a two-level domain decomposition method can be implemented for the EMC applications. The first level decomposition is implemented with MSDDM, in which the original problem is decomposed according to their geometrical properties. For the platform sub-domains with large electrical size, the IEDDM is applied and it automatically decomposes the surface into smaller sub-domains to fit into memory. This decomposition can be totally transparent to the user. With the method developed in this work, the antenna coupling problem on an mock-up aircraft platform of more than 700λ0 was successfully conducted on a workstation with 48GB memory.
Mathematically, the IEDDM slightly enlarges the function space for conventional EFIE formulation, which supports the normal discontinuity at the boundary. The continuity is weakly enforced by testing the residual by Galerkin method. The validity of this formulation has been tested. And it paves the way to IEDG in which diverse basis functions can be hybridized into IE solver.