## Berichte der Arbeitsgruppe Technomathematik (AGTM Report)

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#### Year of publication

- 2001 (11) (remove)

#### Document Type

- Preprint (11) (remove)

#### Keywords

- heat equation (2)
- stationary radiative transfer equation (2)
- Associative Memory Problem (1)
- Capacity (1)
- Earth' (1)
- Feed-forward Networks (1)
- Hyperbolic Conservation (1)
- Industrial Applications (1)
- Learnability (1)
- Navier Stokes equation (1)

- 246
- Maximum Entropy Moment Systems and Galilean Invariance (2001)
- In this article, we investigate the maximum entropy moment closure in gas dynamics. We show that the usual choice of polynomial weight functions may lead to hyperbolic systems with an unpleasant state space: equilibrium states are boundary points with possibly singular fluxes. In order to avoid singularities, the necessary arises to find weight functions which growing sub-quadratically at infinity. Unfortunately, this requirement leads to a conflict with Galilean invariance of the moment systems because we can show that rotational and translational invariant, finite dimensional function spaces necessarily consist of polynomials.

- 245
- A Residual Based Error Formula for a Class of Transport Equations (2001)
- We present an exact residual based error formula in natural norms for a class of transport equations.

- 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.

- 243
- Rigorous Navier-Stokes Limit of the Lattice Boltzmann Equation (2001)
- Here we riqorously investigate the diffusive limit of a velocity-discrete Boltzmann equation which is used in the lattice Boltzmann method to construct approximate solutions of the incompressible Navier-Stokes equation.

- 242
- Do Finite Volume Methods Need a Mesh? (2001)
- In this article, finite volume discretizations of hyperbolic conservation laws are considered, where the usual triangulation is replaced of unity on the computational domain.

- 241
- A limiter based on kinetic theory (2001)

- 239
- Wavelets Generated by Layer Potentials (2001)
- By means of the limit and jump relations of classical potential theory the framework of a wavelet approach on a regular surface is established. The properties of a multiresolution analysis are verified, and a tree algorithm for fast computation is developed based on numerical integration. As applications of the wavelet approach some numerical examples are presented, including the zoom-in property as well as the detection of high frequency perturbations. At the end we discuss a fast multiscale representation of the solution of (exterior) Dirichlet's or Neumann's boundary-value problem corresponding to regular surfaces.

- 238
- Mathematical Theory of Neutral Networks (2001)

- 237
- Part1: Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Scalar Fields; Part2: Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields (2001)
- Abstract: The basic concepts of selective multiscale reconstruction of functions on the sphere from error-affected data is outlined for scalar functions. The selective reconstruction mechanism is based on the premise that multiscale approximation can be well-represented in terms of only a relatively small number of expansion coefficients at various resolution levels. A new pyramid scheme is presented to efficiently remove the noise at different scales using a priori statistical information.