Catálogo de publicaciones - libros

We present a modification of a well-known mathematical model based on the Rigorous Coupled-Wave Analysis (RCWA) that can be used to solve optical diffraction problems on periodic structures (both 1-D and 2-D gratings with approximated layer-structure). The algorithm calculates the reflected and transmitted field which in turn determine the diffraction efficiencies for all reflected and transmitted orders.

Results created with a Matlab implementation of the modified RCWA algorithm (MSolver) show excellent overlap with other published and measured data.

One of the fields of engineering science in which numerical simulation is playing a role of increasing importance is the design of piezoelectric transducers. Efficient techniques to solve the forward problem of computing the mechanical displacements and electric potential for a given configuration play a crucial role in the design itself, but also in the related problem of identifying the correct material parameters. In this paper we consider the iterative solution of linear systems arising from a Finite-Element discretisation of the piezoelectric forward problem with the Generalised Minimal Residual method in combination with incomplete LU decomposition and inexact block diagonal preconditioning.

Transport phenomena in a submicron silicon bipolar junction transistor are described by using an extended hydrodynamic model for the electrons, combined with a solution of the drift-diffusion model for the holes. Under suitable scaling assumptions, the above model reduces to the energy transport model, or to the Navier-Stokes-Fourier model, in which all the transport coefficients are now explicitly determined. The validity of the constitutive equations is investigated by using Monte Carlo simulations.

In radio frequency (RF) application, electric circuits often exhibit multitone signals, where time scales differ by several orders of magnitude. Thus circuit simulation by means of transient analysis becomes inefficient. A multivariate model yields an alternative strategy considering amplitude as well as frequency modulation. Consequently, a warped multirate partial differential algebraic equation (MPDAE) has to be solved using periodic boundary conditions. Thereby, the determination of a local frequency function is crucial for the efficiency of the model. For this purpose, two special choices of continuous phase conditions are applied as additional boundary conditions. Numerical simulations show that these continuous phase conditions identify local frequency functions, which are physically reasonable.

The maximum entropy moment systems of the Boltzmann equation is only solvable with physically unrealistic restrictions on the choice of the macroscopic variables. We show that no such difficulties appear in the semiconductor case if Kane’s dispersion relation is used for the energy band of electrons. As an application the 5-moment model is discussed.

Two main approaches are known for the reduced order modelling of linear time-invariant systems: Krylov subspace based and SVD based approximation methods. Krylov subspace based methods have large scale applicability, but do not have a global error bound. SVD based methods do have a global error bound, but require full space matrix computations and hence have limited large scale applicability. In this paper features and short-comings of both types of methods will be addressed. Furthermore, ideas for improvements will be discussed and the possible application of Jacobi-Davidson style methods such as JDQR and JDQZ for model reduction will be considered.

This paper presents a new Runge-Kutta type integration method that is well-suited for time-domain simulation of oscillators. A unique property of the new method is that its damping characteristics can be controlled by a continuous parameter.

Adaptive stepsize control is used to control the local errors of the numerical solution. For optimization purposes smoother stepsize controllers are wanted, such that the errors and stepsizes also behave smoothly. We consider approaches from digital linear control theory applied to multistep BDF-methods.

The stabilization of a Bunsen flame above the burner rim is simulated using the method of characteristics. Oscillations of the flame front and of its area due to flow oscillations are computed.

A generalized deffinition is given for the time index and a new prototype example is introduced, which serves as a general case for the computation of the time index for a hierarchy of molten carbonate fuel cell models, including a 2D model. The time indices are computed by a new approach using linear integral equations.