Biography
Prof. Klaus G
Prof. Klaus G"artner
m4sim GmbH, Germany
Abstract: 
Particle systems on earth can cover a pretty large range of particle energies (from meV in biology to MeV in nuclear physics), are often approximately described by large systems of elliptic or parabolic equations and have a common starting point: the Boltzmann equation and the H-theorem, which naturally involve the concept of dissipation and a free energy functional, decaying along solutions in time.
Assuming some differntiability of the solutions and a shortest time scale (the smallest collision time) one ends very often up with 'diffusion  
approximations', that are valid outside a ball of 'three mean free flight paths' around all 'points of interest' (point sinks/sources, ..., material interfaces, non convex domains) and result in a dramatic reduction of complexity in large parts of the domain by replacing $v$, the velocity vector of a particle by its energy and keeping space and time coordinates together with the assumption: all collisions are dissipative in total for solutions - hence: neglecting some details never creates energy.

In case a special energy distribution is known for all time scales of interest above a critical shortest time, one calls the special situation 'Boltzmann-' or 'Fermi-statistics' and the variables are a finite number of species (or chemical potentials), their space coordinates, special interactions (e.g. an electrostatic potential acting on charged particles) and time.

For approximations with a large range of validity the related discrete equations have to fulfill the same qualitative properties as their analytic counterparts.

The setting is rather general, but it does not cover 'hyperbolic conservation laws', and the arguments used to derive them for large time scales are often questionable.

This concept is the basic assumption of the talk and it is illustrated using different semiconductor problems where we should have no need to go
beyond the assumptions as long as we want to describe devices with reproducible behavior with a probability of $1-\epsilon$, $\epsilon << 1$ for given boundary conditions and time scales large compared with free flight times.

The discrete versions of the equations can be chosen such that the qualitative properties of the analytic problem are preserved. The approximation order is limited due to the natural smoothness properties of the problem.
Biography: 
Born 1950 at Zittau, East Germany, I grew up in at the nearby village Hainewalde where my father worked as MD. After finishing the local school, I got the high-school diploma with excellence at Zittau, studied theoretical physics at Technical University Dresden and moved with Prof. K. Meyer (a Steenbeck pupil) to Zittau Technical college for a PhD in nuclear reactor theory (1968 stirred up the East, too). After submission I worked at Berlin in an industrial research department (interrupted by national service) on neutron transport in fast breeders until 1982 and joint the Institute of Mathematics of the Academy of Sciences numerics group at Mohrenstrasse (Prof. Grund).

Electron transport in semiconductors, in a close collaboration with Analysis people led by Prof. Gajewski, was the new field. After the wall came down I went to the IPS (Prof. M. Gutknecht) of ETH Zurich in 1992 and changed later to IIS (Prof.  W. Fichtner). The pardiso project started as part of the Cray/ETH collaboration (with the PhD student O. Schenk). The collaboration with Gajewski continued and resulted in stability and further results for the weak, finite volume form of the van Roosbroeck's equations. It was the basis to return to Berlin (WIAS, Mohrenstrasse same building) in 1998.
Degenerate parabolic equations, their discretization and numerical  solution have been the main topics, Delaunay meshes (PhD Hang Si) and pardiso evolved further until 2015/16, as $A{-1} B A{-H}$ was included for NGEF (or Keldysh formalism, struc(A)= struct(B), A, B sparse, A regular) applications.
The HLL of the MPG at Munich collaborated on pretty complex, silicon based DEPFET detectors, e.g., including data compression per pixel, based on Oskar3, my 'experimental algorithmic' 3d device simulator.
In 2018 the WIAS-spin-off m4sim was founded to extend Delaunay meshing and solution methods. 3d IGBTs, e.g., are very demanding: from adaptive Delaunay meshes to special damping methods for singular perturbed solutions --  Covid was not helpful all -- but a lot of interesting questions showed up ...