A numerical algorithm for the solution of the two-dimensional effective mass Schrödinger equation for current-carrying states is developed. Boundary conditions appropriate for such states are developed and a solution algorithm constructed that is based on the finite element method. The utility of the technique is illustrated by solving problems relevant to submicron semiconductor quantum device structures.

This paper presents an analysis of several methods for approximately solving the equations governing multicomponent mass transport with homogeneous and heterogeneous chemical reactions. A derivation of the governing equations allowing a fairly general description of the chemistry is given. It is shown that a number of different formulations are possible depending on the choice of primary variables. Discretization of the governing equations reduces the problem to solving a set of nonlinear algebraic equations each time step. It is shown that the choice of method to solve the algebraic equations should be based on the nature of the chemical reactions. An analysis of the equations yields recommendations in some cases and direction for numerical experimentation in others.

A technique is described for modeling the groundwater transport of a multicomponent solution of metals and ligands. By this method both soluble complexation and competitive sorption among chemical species may be accommodated. A finite element solution is presented for an arbitrary number of components. It is shown that although this technique leads to strongly nonlinear equations, accurate solutions may still be achieved. It is also shown that the interaction mechanisms modeled can have significant impact on the transport potential of solution components.

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