Stefan Schäffler

Adams methods for the efficient solution of stochastic differential equations with additive noise

The application of Adams methods for the numerical solution of stochastic differential equations is considered. Especially we discuss the path-wise (strong) solutions of stochastic differential equations with additive noise and their numerical computation. The special structure of these problems suggests the application of Adams methods, which are used for deterministic differential equations very successfully. Applications to circuit simulation are presented.

Transient Noise Simulation: Modeling and Simulation of 1/f -Noise

In this paper we present a new approach for the transient noise simulation of electronic circuits with stochastic differential algebraic equations (SDAEs). The first part treats the modeling of noise in the time domain which is accomplished with generalized stochastic processes. This allows not only to model white noise like thermal and shot noise, but also 1/f-noise or flicker noise. It is shown that fractional Brownian motion reflects the properties of 1/f -noise, namely a spectrum proportional to 1/f with f denoting the frequency. Some consequences of this approach on the solvability of the circuit equations are presented. In the second part we give remarks on the implementation of numerical schemes for SDAEs. Besides the integration scheme itself the generation of appropriate random numbers is a major issue. Finally we present some numerical experiments.

A Stochastic Method for Constrained Global Optimization

A stochastic method is described for solving constrained global optimization problems using a penalty approach. Interesting properties and a parallel implementation of the algorithm enable the treatment of problems with a large number of variables.

Global Minimization of Lennard-Jones Functions on Transputer Networks

This paper presents a three-phase computational procedure for minimizing molecular energy potential functions of the pure Lennard-Jones type. The first phase consists of a special heuristic for generating an initial atomic configuration. In the second phase a global minimization method is applied to compute a configuration close to the optimal solution. Finally, the third phase uses this configuration as the starting point for a local minimization method. Since the second and third phases are very suitable for parallel implementation, we describe briefly our implementation of the method in a parallel version of C on a transputer network, and we exhibit numerical results for approximate optimization of clusters with up to 20,000 atoms.

Large-Scale Global Optimization on Transputer Networks

This paper presents a stochastic method for solving large-scale global optimization problems. An efficient algorithm is developed and investigated. Since this algorithm is very suitable for parallel implementation, an implementation of the method in a parallel version of C on a transputer network is briefly described. Numerical results for optimization problems in up to 60,000 variables are considered.

A Fuzzy Set Approach for Optimal Positioning of a Mobile Robot Using Sonar Data

A procedure for optimal positioning of a mobile robot based on sonar data is presented. This procedure uses simulated sonar scan data in order to gain step by step information about the unknwon room, which is modelled as a fuzzy set. The definition and application of a special measure allows the calculation of a new position, which promises the maximal amount of additional information about the unknown room, if the new position is interpreted as the next scan position. The efficiency of the algorithm is shown by examples.