Research On Higher-Order Method Of Moments Based On Bézier Quadrangular Patches

The method of moments is one of important methods to analyze electromagnetic problems based on integral equations. The traditional method of moments uses usually the RWG basis functions. Due to the supports of the RWG basis functions being planar triangular pairs and the RWG basis functions being of lower order, the object surface must be divided into many small pieces, sizes of which being about 0.1 wavelength. Therefore, the unknowns generated by the method of moments are very much, resulting in very high computational complexity and storage complexity. To overcome this shortcoming, many fast algorithms based on the method of moments have been developed, significantly reducing both the computational complexity and storage complexity. Another way to reduce both the computational complexity and storage complexity is to introduce higher-order basis functions defined on curved surface patches into the method of moments. In this way, the mesh scale can be increased with the increase of the order of higher-order basis functions, which can also significantly reduce the number of unknowns and hence both the computational complexity and storage complexity. At present, the research on the higher-order method of moments has become a hot topic in computational electromagnetism. Here we mainly study the higher-order method of moments (HMoM) based on Bézier curved surface quadrangle modeling, will establish an acceleration scheme for the HMoM based on ACA matrix compression and build a multi-core CPU parallel version of the HMoM. The main works of this Master Dissertation are as follows:1. The Bézier curved quadrilateral subdivision on the surface of an object has done. The the-oretical and experimental analysis have verified the Bézier curved quadrilateral subdivi-sion model through the comparison with the conventional Lagrange interpolation curved quadrilateral subdivision model. With the increase of order, the accuracy of Bézier curved quadrilateral subdivision model is obviously better than the Lagrange interpolation curved quadrilateral subdivision model.2. A new higher-order hierarchical vector basis functions based on Legendre basis functions on Bézier curved quadrilateral surfaces has proposed for the method of moments in Com-putational Electromagnetics. Such higher-order hierarchical vector basis functions are of quasi-orthogonality, and not only have higher accuracy in geometric surface simula-tion, but also can accurately describe the equivalent surface current. Accordingly, such higher-order basis functions can generate a well-conditioned HMoM matrix. Numerical examples provided in this dissertation have verified the accuracy of this HMoM.3. A scheme for accelerating the HMoM by using ACA matrix compression has established. By means of the octree structure, we distinguish between near-field and far-field interac-tions, and apply ACA compression technology to each of the sub-matrices generated by well-separated groups. This method can reduce the matrix storage and accelerate calcu-lating matrix-vector product. Some numerical examples provided in this dissertation have verified the feasibility of this acceleration scheme.4. A parallel version for the HMoM in this dissertation on a multi-core CPU platform has realized.