Study Of Electromagnetic Integral Equations Of Meshless Method

The traditional numerical methods used to solve electromagnetic computational problems need to define a set of basis functions on a simplicial discretization of the geometry of the objects to characterize the unknown field quantity. These basis functions used for vector electromagnetic formulations have been designed to invoke special properties across internal boundaries of the discrete elements. Because these basis functions are intimately related to the discretization of the geometry, over-discretization and numerous unknowns will make the computation very slow. If the contact between the elements can be relaxed, it would be possible to break through the bottleneck of the mesh analysis method. At the same time, if the close ties between the basis functions and the meshing of the geometry can be eliminated, numerical analysis can mix different orders and different types of basis functions. To achieve these purposes utilizing meshless method is very promising.In this thesis, the radial basis function (RBF) based meshless method (MLM) is used to analysis electromagnetic scattering problems. When the RBF is used, it is easy to impose the essential boundary conditions to Maxwell’s equations, and also not have to create the background grid for integral calculation. Another meshless method which is based on the partition of unity method (PUM), also known as the generalized method of moments, make the shape function as a function of the product of partition of unity and approximation functions, also has been proposed in this thesis. Since the selection of the approximation functions is not limited, the PUM based meshless method defines the type of shape functions is more flexible than the RBF based meshless method.First, this thesis introduces some basic theory in electromagnetic numerical calculation method. Then we introduce the implementation process of the RBF based meshless method, and apply this method to analyze electromagnetic scattering of2-D and3-D PEC targets. Next, the adaptive cross approximation (ACA) algorithm is combined with the RBF based meshless method to analyze electromagnetic scattering of objects with large electrical size. The memory requirements and computational complexity is remarkably reduced when the ACA is applied. Finally, the PUM based MLM is applied to analyze the electromagnetic scattering problems of the microstrip structure.