Duration: | Since May 2003 |
Project leader: | A. Unterreiter |
Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany | |
Tel: +49 (0)30 - 314 24884 (office) / - 314 24351 (secretary) | |
email: unterreiter@math.tu-berlin.de | |
Project member: | R. Plato |
Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany | |
Tel: +49 (0)30 - 314 25743 | |
email: plato@math.tu-berlin.de | |
Cooperations: | A. Jüngel, Universität Mainz |
R. Pinnau, TU Darmstadt | |
S. Volkwein, TU Graz | |
Support: | DFG Research Center "Mathematics for Key Technologies" |
It is the main aim of the proposed research project to exploit and to extend entropy methods to simulate and to optimize transient performances of semiconductor devices. In particular it is planned to derive decay rates for "discrete" entropies associated with numerical schemes and to optimize semiconductor's doping profiles with respect to desired equilibrium states and with respect to entropy decay rates. First results on that topic are given in reference [4]. Investigations are in progress. | |
Another important feature is the calibration of drift-diffusions models, i.e., the determination of the coefficients of the system. Applications are, e.g., the determination of prices for options in the financial markets. Those problems can be decomposed into two subproblems. One of these two subproblems is the solution of Volterra integral equations of the first kind. Those problems can be efficiently and stably solved by multistep methods as it shown in reference [3]. |
[1] | A. Arnold and A. Unterreiter |
Entropy decay of discretized Fokker-Planck equations - temporal semi-discretization. , "Journal of Computational and Applied Mathematics". Abstract | |
[2] | M. Ramaswami and A. Unterreiter |
Generalized Hardy-Sobolev inequalities and exponential decay of the Entropy of degenerated parabolic equations, to appear in "Monatshefte für Mathematik". | |
[3] | R. Plato |
Fractional multistep methods for weakly singular Volterra integral equations of the first kind with perturbed data. Preprint DFG FZT No. 4. | |
[4] | A. Jüngel and A. Unterreiter |
Discrete Minimum and Maximum Principles for Finite Element Approximations of Non-Monotone Elliptic Equations. Preprint DFG FZT No. 42. | |
[5] | R. Plato |
Large time asymptotics for a fully discretized Fokker-Planck type equation. Preprint DFG FZT No. 137. |
[1] | R. Plato | Regularization of weakly singular Volterra equations by fractional multistep methods | 20th Biennial Conference on Numerical Analysis, Dundee, June 2003. |
[2] | R. Plato | Entropie estimates for Fokker-Planck equations. | Gamm conference, Dresden, March 2004. |
[3] | A. Unterreiter | Optimal Control of the Stationary Quantum Drift-Diffusion Model | EUCCO conference, Dresden, March 2004. |
[4] | R. Plato | Large time asymptotics for Fokker-Planck equations. | Conference Modern Computational Methods in Applied Mathematics, Bedlewo, June 2004. |
R. Plato | Concise Numerical Mathematics , AMS, Rhode Island, 460 pages, 2003. | |
R. Plato | Numerische Mathematik kompakt, 2. edition , Vieweg Verlag, Wiesbaden, 410 pages, appears in August 2004. | |
R. Plato | Übungsbuch zur Numerischen Mathematik , Vieweg Verlag, Wiesbaden, 220 pages, appears in September 2004. |