Application of wavelets in computational electromagnetics and semiconductor device modeling

Two new approaches introducing wavelets to computational electromagnetics and semiconductor device modeling are presented in this dissertation.; In the first approach, the Coifman wavelets are employed to perform Galerkin's procedure in the method of moments (MoM). The Coiflets are continuous, smooth, overlapping, yet orthogonal; which permit significant reduction of the sampling rate and dramatic compression of the matrix size with respect to the pulse based MoM. The vanishing moments of the Coiflets of order L = 4 provide high precision O(h5) one-point quadrature, which knocks down the computational effort in filling the matrix entries from O(n2) to O(n). This new approach has been applied to solve the scattering problem of very rough surfaces. As an electrically large problem; it was solved originally on a supercomputer with moderate success. However, the new approach achieves great saving of computational effort. Numerical results from the new approach are in good agreement with the experimental measurements.; The second new approach is to use multiwavelets in the finite element method (FEM) for electromagnetic wave problems and semiconductor device simulations. In this multiwavelets finite element method (MWFEM) approach, the multiscalets (multiscaling functions) are employed as the basis functions. Because of the interpolatory property of the multiscalets in terms of the basis function and its derivatives, fast convergence in approximating a function is achieved.; The multiscalets and their derivatives are orthonormal in the discrete sampling nodes. Therefore, no coupled system of equations in terms of the function and its derivative is involved, resulting in a simple and efficient algorithm. In the example of a partially loaded waveguide problem, a memory saving of 16 and CPU performance acceleration of 400 over the conventional linear EEM is achieved.; Due to the ability of MWFEM to track the tendency, namely; the first derivative of the unknown function, the MWFEM remains stable in the highly nonlinear systems and is therefore suitable for semiconductor simulation in which the conventional FEM and finite difference (FD) schemes always result in oscillatory results. Numerical examples of the MWFEM in both widely used drift-diffusion model and more advanced Boltzmann transport equation (BTE) model demonstrate high efficiency and accuracy of the new method.