Multiwavelets in solving nonlinear transport equations

Modeling and simulation of semiconductor devices deal with highly nonlinear equations, such as the drift-diffusion, hydrodynamic, and Boltzmann transport. equations. The multiwavelet based finite element method (MWFEM) is introduced and applied to 1D drift-diffusion device simulation. The mutual orthogonality of the multiwavelets in terms of a function and its first, second (and so forth) derivatives permits the derivation of an uncoupled algebraic system to solve the unknown coefficients of the functional expansion. As a result, the MWFEM tracks the unknown function along with its tendency. Hence, the spurious oscillation of the conventional FEM is eliminated. A numerical example demonstrates that the new method achieves high accuracy and stability for Poisson´s equation coupled with the nonlinear drift-diffusion equation with small to large Reynolds numbers. Versatility of the new algorithm encourages its use in complex systems of the Boltzmann, Wigner and non-equilibrium Green´s function based transport equations.