We present a general technique to solve one-dimensional time-dependent Schrödinger-type equations. A mapped infinite elements approach is used to eliminate spurious reflections of outgoing wave packets from the boundaries of the interval of interest. This procedure leads to more precise solutions because the space coordinates are discretized to approximate the solution in the entire physical domain. We show its utility giving numerical results on three typical examples: a bounded short-range potential; the unbounded potential of a particle in a dc field; and a Hamiltonian with an intrinsic time dependence like the Hamiltonian of a charged particle in an ac electromagnetic field.
This paper presents the implementation of the finite element method combined with Dirichlet-to-Neumann (DtN) mapping (derived in terms of an infinite Fourier series) for studying the solvability of an exterior problem arising in linear incomepressible 2D-elasticity. A reliable numerical experiment is also presented showing the accuracy of DtN mapping; only a few Fourier series terms were needed to get a good approximation to the solution. The stable Taylor-Hood element was used for finite element discretisation.
A multigrid (MG) numerical solution procedure for a mathematical model for epitaxial growth in metalorganic chemical vapor deposition reactors is developed. The model is governed by the full compressible Navier–Stokes equations for two-dimensional (plane and axisymmetric) laminar flows extended by transport equations for the chemical species, the energy equations and the equation of state, together with boundary conditions providing information on the reactor geometry and experimental conditions. The MG numerical solution is implemented in a finite element procedure that uses the same linear finite elements to discretize both convection and diffusion fluxes by adding to the model a stabilizing term, resulting in easy implementation of the procedure. A deposition process for a model of GaAs growth is calculated with our procedure showing consistency with experimental data.
We propose a stable finite element method for approximating the flow of a chemically reacting gas mixture in an MOCVD (metal-organic chemical vapor deposition) reactor. The flow is governed by the full compressible Navier-Stokes equations extended by transport equations for the chemical species, the energy equations and the equation of state, together with boundary conditions providing information on the reactor geometry and experimental conditions. The equations form a semilinear system with a constraint for which the corresponding pressure term is not the Lagrangian multiplier. An application of our method to a real world model of growth of GaAs shows the consistency with experimental data.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.