Efficient wave function matching approach for quantum transport calculations

The Wave Function Matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable with the widely used Green's function approach. The WFM formalism presented so far requires the evaluation of all the propagating and evanescent bulk modes of the left and right electrodes in order to obtain the correct coupling between device and electrode regions. In this paper we will describe a modified WFM approach that allows for the exclusion of the vast majority of the evanescent modes in all parts of the calculation. This approach makes it feasible to apply iterative techniques to efficiently determine the few required bulk modes, which allows for a significant reduction of the computational expense of the WFM method. We illustrate the efficiency of the method on a carbon nanotube field-effect-transistor (FET) device displaying band-to-band tunneling and modeled within the semi-empirical Extended H\"uckel theory (EHT) framework.Comment: Submitted to Phys. Rev.

Verified global optimization for estimating the parameters of nonlinear models

Nonlinear parameter estimation is usually achieved via the minimization of some possibly non-convex cost function. Interval analysis allows one to derive algorithms for the guaranteed characterization of the set of all global minimizers of such a cost function when an explicit expression for the output of the model is available or when this output is obtained via the numerical solution of a set of ordinary differential equations. However, cost functions involved in parameter estimation are usually challenging for interval techniques, if only because of multi-occurrences of the parameters in the formal expression of the cost. This paper addresses parameter estimation via the verified global optimization of quadratic cost functions. It introduces tools for the minimization of generic cost functions. When an explicit expression of the output of the parametric model is available, significant improvements may be obtained by a new box exclusion test and by careful manipulations of the quadratic cost function. When the model is described by ODEs, some of the techniques available in the previous case may still be employed, provided that sensitivity functions of the model output with respect to the parameters are available

Exploiting the natural partitioning in the numerical solution of ODE systems arising in atmospheric chemistry

. Large air pollution models are commonly used to study transboundary transport of air pollutants. Such models are described mathematically by systems of partial differential equations (the number of equations being equal to the number of pollutants involved in the model). The use of appropriate splitting procedures leads to several sub-models. If the model is discretized on a (96x96x10) grid and if the number of pollutants is 35, then a system of ODE's containing 3225600 equations is to be treated in each sub-model. The chemical sub-model consists of (96x96x10) ODE systems, each of them containing 35 equations. The number of time-steps, needed in each sub-model, is typically several thousand. The chemical part of an air pollution model is one of the most difficult parts for the numerical algorithms. Therefore it is desirable to apply reliable and sufficiently accurate algorithms during the numerical treatment of the chemical sub-models. Moreover, it is also desirable to a..

Stability of Backward Euler Multirate Methods and Convergence of Waveform Relaxation ∗

For a large class of traditional backward Euler multirate methods we show that stability is preserved when the methods are applied to certain stable (but not necessarily monotonic) non-linear systems. Methods which utilize waveform relaxation sweeps are shown to be stable and converge for certain monotonic systems. 1 Relaxing the monotonicity condition Consider the system of ODE’s (i.e. ordinary differential equations) y ′ = f(t, y) for t ≥ t0, where y(t) ∈ ℜ s. (1.1) In order to prove stability of numerical methods applied to (1.1), some type of monotonicity condition is usually imposed on the system of ODE’s, i.e. a condition ensuring the existence of a norm such that � u(t2) − v(t2) �≤ � u(t1) − v(t1) � for t2 ≥ t1 ≥ t0, (1.2) holds for any two solutions u and v of (1.1). Most often it is assumed that the norm can be chosen as an inner-product norm, but an example by Spijker ([1, p. 658]): y ′

atmospheric chemistry

Exploiting the natural partitioning in th