## Fachbereich Mathematik

### Refine

#### Faculty / Organisational entity

- Fachbereich Mathematik (881)
- Fraunhofer (ITWM) (2)

#### Year of publication

#### Document Type

- Preprint (566)
- Doctoral Thesis (193)
- Report (39)
- Article (28)
- Diploma Thesis (25)
- Lecture (18)
- Part of a Book (4)
- Study Thesis (4)
- Working Paper (2)
- Bachelor Thesis (1)

#### Has Fulltext

- yes (881) (remove)

#### Keywords

- Wavelet (12)
- Inverses Problem (10)
- Modellierung (10)
- Mathematikunterricht (9)
- Mehrskalenanalyse (9)
- praxisorientiert (9)
- Boltzmann Equation (7)
- Location Theory (7)
- Approximation (6)
- Lineare Algebra (6)

- The Stationary Current-Voltage Characteristics of the Quantum Drift Diffusion Model (1999)
- This paper is concerned with numerical algorithms for the bipolar quantum drift diffusion model. For the thermal equilibrium case a quasi-gradient method minimizing the energy functional is introduced and strong convergence is proven. The computation of current - voltage characteristics is performed by means of an extended emph{Gummel - iteration}. It is shown that the involved fixed point mapping is a contraction for small applied voltages. In this case the model equations are uniquely solvable and convergence of the proposed iteration scheme follows. Numerical simulations of a one dimensional resonant tunneling diode are presented. The computed current - voltage characteristics are in good qualitative agreement with experimental measurements. The appearance of negative differential resistances is verified for the first time in a Quantum Drift Diffusion model.

- A Finite Difference Interpretation of the Lattice Boltzmann Method (1999)
- Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be a completely different approach to solve the incompressible Navier-Stokes equations. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side effect, new starting points for a discretization of the incompressible Navier-Stokes equations are obtained.

- Remarks on Orthogonal Polynomials and Balanced Realizations (1992)
- Given a proper antistable rational transfer function g, a balanced realization of g is contructed as a matrix representation of the abstract shift realization introduced in Fuhrmann [1976]. The required basis is constructed as a union of sets of polynomials orthogonal with respect to weights given by the square of the absolute values of minimal degree Schmidt vectors of the corresponding Hankel operators. This extends results of Fuhrmann [1991], obtained in the generic case.

- An Analysis of Baganoff" s Shuffle Algorithm (1993)
- The paper presents the shuffle algorithm proposed by Baganoff, which can be implemented in simulation methods for the Boltzmann equation to simplify the binary collision process. It is shown that the shuffle algborithm is a discrete approximation of an isotropic collision law. The transition probability as well as the scattering cross section of the shuffle algorithm are opposed to the corresponding quantities of a hard-sphere model. The discrepancy between measures on a sphere is introduced in order to quantify the approximation error by using the shuffle algorithm.

- Construction of Particlesets to Simulate Rarefied Gases (1993)
- In this paper a new method is introduced to construct asymptotically f-distributed sequences of points in the IR^d. The algorithm is based on a transformation proposed by E. Hlawka and R. Mück. For the numerical tests a new procedure to evaluate the f-discrepancy in two dimensions is proposed.

- Domain Decomposition: Linking Kinetic and Aerodynamic Descriptions (1993)
- We discuss how kinetic and aerodynamic descriptions of a gas can be matched at some prescribed boundary. The boundary (matching) conditions arise from requirement that the relevant moments (p,u,...) of the particle density function be continuous at the boundary, and from the requirement that the closure relation, by which the aerodynamic equations (holding on one side of the boundary) arise from the kinetic equation (holding on the other side), be satisfied at the boundary. We do a case study involving the Knudsen gas equation on one side and a system involving the Burgers equation on the other side in section 2, and a discussion for the coupling of the full Boltzmann equation with the compressible Navier-Stokes equations in section 3.

- Fast Generation of Low-Discrepancy Sequences (1993)
- The paper presents a fast implementation of a constructive method to generate a special class of low-discrepancy sequences which are based on Van Neumann-Kakutani tranformations. Such sequences can be used in various simulation codes where it is necessary to generate a certain number of uniformly distributed random numbers on the unit interval.; From a theoretical point of view the uniformity of a sequence is measured in terms of the discrepancy which is a special distance between a finite set of points and the uniform distribution on the unit interval.; Numerical results are given on the cost efficiency of different generators on different hardware architectures as well as on the corresponding uniformity of the sequences. As an example for the efficient use of low-discrepancy sequences in a complex simulation code results are presented for the simulation of a hypersonic rarefied gas flow.

- 3D Eddy-Current Computation Using Krylov Subspace Methods (1993)
- This paper considers the numerical solution of a transmission boundary-value problem for the time-harmonic Maxwell equations with the help of a special finite volume discretization. Applying this technique to several three-dimensional test problems, we obtain large, sparse, complex linear systems, which are solved by using BiCG, CGS, BiCGSTAB resp., GMRES. We combine these methods with suitably chosen preconditioning matrices and compare the speed of convergence.