Wavelet-based Galerkin method for semiconductor devices simulation

Using wavelet methods, local high order schemes can be constructed near the singularities. Moreover, the stiffness matrix is sparse and can readily be inverted due to the compact support property of wavelets. An adaptive Galerkin-wavelet method for semiconductor devices simulation is presented. A set of wavelet bases can be chosen adaptively for each iteration according to the error levels. So, computational time is saved and hence a more accurate result can be obtained by including higher order terms. Also, an elegant way to handle the boundary conditions is provided. A simulation of an abrupt P-N junction is used to demonstrate this effectiveness in this paper