## Berichte der Arbeitsgruppe Technomathematik (AGTM Report)

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#### Keywords

- Boltzmann Equation (7)
- Numerical Simulation (5)
- Elastoplastizität (4)
- Elastoplasticity (3)
- Hysterese (3)
- lattice Boltzmann method (3)
- low Mach number limit (3)
- Elastic BVP (2)
- Elastisches RWP (2)
- Elastoplastisches RWP (2)

- 94
- 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.

- 60
- A 2-D Kaniel Kinetical Scheme for the Isentropic Compressible Flow (1991)
- We have presented here a two-dimensional kinetical scheme for equations governing the motion of a compressible flow of an ideal gas (air) based on the Kaniel method. The basic flux functions are computed analytically and have been used in the organization of the flux computation. The algorithm is implemented and tested for the 1D shock and 2D shock-obstacle interaction problems.

- 46
- A Comparison of a Microscopic and a Phenomenological Model for a Polyatomic Gas (1990)
- Treating polyatomic gases in kinetic gas theory requires an appropriate molecule model taking into account the additional internal structure of the gas particles. In this paper we describe two such models, each arising from quite different approaches to this problem. A simulation scheme for solving the corresponding kinetic equations is presented and some numerical results to 1D shockwaves are compared.

- 91
- A Comparison of Simulation Methods for Rarefied Gas Flows (1993)
- Simulation methods like DSMC are an efficient tool to compute rarefied gas flows. Using supercomputers it is possible to include various real gas effects like vibrational energies or chemical reactions in a gas mixture. Nevertheless it is still necessary to improve the accuracy of the current simulation methods in order to reduce the computational effort. To support this task the paper presents a comparison of the classical DSMC method with the so called finite Pointset Method. This new approach was developed during several years in the framework of the European space project HERMES. The comparison given in the paper is based on two different testcases: a spatially homogeneous relaxation problem and a 2-dimensional axisymmetric flow problem at high Mach numbers.

- 271
- A condition that a continuously deformed, simply connected body does not penetrate itself (2007)
- In this article we give a sufficient condition that a simply connected flexible body does not penetrate itself, if it is subjected to a continuous deformation. It is shown that the deformation map is automatically injective, if it is just locally injective and injective on the boundary of the body. Thereby, it is very remarkable that no higher regularity assumption than continuity for the deformation map is required. The proof exclusively relies on homotopy methods and the Jordan-Brouwer separation theorem.

- 42
- A Deterministic Particle Method for the Simulation of the Boltzmann Transport Equation of Semiconductors (1990)
- We present a deterministic simulation scheme for the Boltzmann Semiconductor Equation. The convergence of the method is shown for a simplified space homogeneous case. Numerical experiments, which are very promising, are also given in this situation. The extension for the application to the space inhomogeneous equation with a self consistent electric field is quoted. Theoretical considerations in that case are in preparation.

- 211
- 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.

- 207
- A General Hilbert Space Approach to Wavelets and Its Application in Geopotential Determination (1999)
- A general approach to wavelets is presented within a framework of a separable functional Hilbert space H. Basic tool is the construction of H-product kernels by use of Fourier analysis with respect to an orthonormal basis in H. Scaling function and wavelet are defined in terms of H-product kernels. Wavelets are shown to be 'building blocks' that decorrelate the data. A pyramid scheme provides fast computation. Finally, the determination of the earth's gravitational potential from single and multipole expressions is organized as an example of wavelet approximation in Hilbert space structure.

- 268
- A homotopy between the solutions of the elastic and elastoplastic boundary value problem (2006)
- In this article, we give an explicit homotopy between the solutions (i.e. stress, strain, displacement) of the quasistatic linear elastic and nonlinear elastoplastic boundary value problem, where we assume a linear kinematic hardening material law. We give error estimates with respect to the homotopy parameter.

- 244
- A Hybrid Simulation Method for Radivative Transfer Equations (2001)
- We consider heat transfer processes where radiation in a large number of frequency bands plays a dominant role.