Electromagnetic device modeling using a new adaptive wavelet finite element method

摘要

Wavelets provide sparse representations of integral and differential operators through a multiresolution approximation. This property is well-suited for adaptive implementation of numerical techniques, which is a common topic among researchers nowadays. The current state of the wavelet theory also allows flexible construction of transforms customized to certain applications, which is an important feature considering that the generalization of wavelet techniques to a large class of real-world numerical simulations is still limited. In this paper, it is proposed an adaptive wavelet finite element method for achieving operator-orthogonality between approximation spaces, a property which eliminates coupling among levels of resolution - a common shortcoming of adaptive methods. The resulting method is easily extended to any given finite element application and requires less computation power when compared to other adaptive techniques. These features are showcased by comparing the proposed technique to the popular h-refinement method using electromagnetic device simulations involving Dirichlet and Neumann boundary conditions, inhomogeneous and non-linear media, and irregular meshes.