Efficient Electromagnetic Algorithms For Simulations Of Electrically Large Complex Objects

Efficient and effective simulations for electrically large complex objects are studied in this dissertation. We propose several new theories and methods to improve the computational efficiency compared against the conventional ones while maintaining the accuracy. Innovations of the dissertation are as follows:1. Using the MoM with OpenMP-CUDA technique, it can achieve above 10 times speed-up performance;2. We propose fast algorithms combined with robust preconditioners to simulate the electrically-large objects efficiently;3. The MLFMA-PO hybrid methods is invented to solve radiation problems of antennas mounted on platforms. The efficiency is optimized while the accuracy is also maintained.4. We construct the multi-algorithm cooperative computation platform which can support plenty of CEM algorithms. This platform overcomes the limitations of a single algorithm.Firstly, the basic mathematical frameworks of integral equations (IE) and the method of moments (MoM) in Computational Electromagnetics (CEM) are introduced.The parallelized MoM based on OpenMP-CUDA is developed to improve the computational efficiency dramatically. The fast algorithm based on IE are then proposed to further enlarge the capacity of simulation. The fast algorithms include two main categories. The first kind is built on algebraic matrix decomposition theorem. The second kind is based on physical equivalence. Some other aspects of the fast algorithms based on integral equations are studied to efficiently analyze several specified real-world applications. The fast monostatic scattering calculation scheme based on asymptotic wave evaluation (AWE) and algebraic matrix decomposition is stated firstly. The translation invariance motivated algebraic fast algorithm is proposed to compute the periodic structures with much less time and memory usage even compared with MLFMA. The EFIE-CFIE hybrid integral equation and Improved PMCHWT equation are then introduced to efficiently handle the open-close complex objects and homogeneous dielectric structures, respectively.Since the impedance matrices generated from the electrically large complex objects are always ill-conditioned, the robust and strong preconditioning techniques are particularly required for the fast algorithms which are based on iterative solvers. In this dissertation, the null-field generation based preconditioner (NFGP) is proposed and introduced in detail. NFGP is easy to complement and naturally suitable for parallelism. Combined with approximate MLFMA technique, NFGP can be further enhanced for faster convergence rate.Moreover, the simulations for the antennas mounted on big platforms are the representative application of the electrically large complex object computations.MLFMA technique is introduced to decrease the computational complexity of the conventional hybrid MoM-PO method. The equivalent dipole technique based on the fast far-field approximation is further developed to improve the accuracy of the calculation of the coupling from MoM region to PO region. The iterative solving scheme, two-octree structure and the iterative physical optics (IPO) are added to the basic MLFMA-PO framework to enhance the efficiency and accuracy of the hybrid method.Lastly, the real-world electrically large complex objects are always multi-scale,multi-medium and multi-physics. Since one single algorithm's ability is limited,the cooperative computation framework based on equivalence theorem which supports all algorithms is proposed. The original complex objects are divided into several regions according to the different propertied listed above. The best algorithm for the specified electromagnetic problems is chosen for every region. The analogous Jacobi iteration scheme is proposed to analyze the interactions between different regions. By using the proposed solver, the condition number of the original problems can be improved since the sub-solvers are all independent to isolate the different properties. Therefore, the cooperative computation framework can be more efficient than the single algorithm to simulate the electrically large complex objects.The algorithms derived in this dissertation provide several powerful methods for the simulation of the electrically large complex objects. The high-performance software systems and computation platforms developed independently have initial applications in the engineering areas. The theoretical conclusions play solid foundations for the further research in this subject.