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Berlin, Germany

The Zuse Institute Berlin is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem.The ZIB was founded by law as a statutory establishment and as a non-university research institute of the State of Berlin in 1984. In close interdisciplinary cooperation with the Berlin universities and scientific institutions Zuse Institute implements research and development in the field of information technology with a particular focus on application-oriented algorithmic Mathematics and practical Computer science. ZIB also provides high-performance computer capacity as an accompanying service as part of the Network of high performance computers in Northern Germany ).Konrad Zuse, born in Berlin in 1910, is the namesake of the ZIB. Wikipedia.

We propose and analyze an interior point path-following method in function space for state constrained optimal control. Our emphasis is on proving convergence in function space and on constructing a practical path-following algorithm. In particular, the introduction of a pointwise damping step leads to a very efficient method, as verified by numerical experiments. © 2012 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Weber M.,Zuse Institute Berlin
Studies in Classification, Data Analysis, and Knowledge Organization | Year: 2013

In this chapter, PCCAC is described as a special spectral clustering algorithm which is applicable for molecular simulation data. From a mathematical point of view, only PCCAC is able to correctly identify the physical timescales of molecular motion. In order to decrease the statistical error of this timescales analysis, an adaptive clustering algorithm is necessary. © Springer-Verlag Berlin Heidelberg 2013.

Gansel J.K.,Karlsruhe Institute of Technology | Wegener M.,Karlsruhe Institute of Technology | Burger S.,Zuse Institute Berlin | Linden S.,Karlsruhe Institute of Technology
Optics Express | Year: 2010

We have recently shown that metamaterials composed of three-dimensional gold helices periodically arranged on a square lattice can be used as compact "thin-film" circular polarizers with one octave bandwidth. The physics of the motif of these artificial crystals is closely related to that of microwave sub-wavelength helical antennas in end-fire geometry. Here, we systematically study the dependence of the metamaterial's chiral optical properties on helix pitch, helix radius, two-dimensional lattice constant, wire radius, number of helix pitches, and angle of incidence. Our numerical calculations show that the optical properties are governed by resonances of the individual helices, yet modified by interaction effects. Furthermore, our study shows possibilities and limitations regarding performance optimization. © 2010 Optical Society of America.

Berthold T.,Zuse Institute Berlin
Mathematical Programming Computation | Year: 2014

This article introduces rens, the relaxation enforced neighborhood search, a large neighborhood search algorithm for mixed integer nonlinear programs (MINLPs). It uses a sub-MINLP to explore the set of feasible roundings of an optimal solution x̄ of a linear or nonlinear relaxation. The sub-MINLP is constructed by fixing integer variables xj with ε Z and bounding the remaining integer variables to xj ε {x̄j, x̄j}. We describe two different applications of rens: as a standalone algorithm to compute an optimal rounding of the given starting solution and as a primal heuristic inside a complete MINLP solver. We use the former to compare different kinds of relaxations and the impact of cutting planes on the so-called roundability of the corresponding optimal solutions. We further utilize rens to analyze the performance of three rounding heuristics implemented in the branch-cut-and-price framework scip. Finally, we study the impact of rens when it is applied as a primal heuristic inside scip. All experiments were performed on three publicly available test sets of mixed integer linear programs (MIPs), mixed integer quadratically constrained programs (MIQCPs), and MINLP s, using solely software which is available in source code. It turns out that for these problem classes 60 to 70 % of the instances have roundable relaxation optima and that the success rate of rens does not depend on the percentage of fractional variables. Last but not least, rens applied as primal heuristic complements nicely with existing primal heuristics in scip. © 2013 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Weiser M.,Zuse Institute Berlin
BIT Numerical Mathematics | Year: 2014

Spectral deferred correction methods for solving stiff ODEs are known to converge reasonably fast towards the collocation limit solution on equidistant grids, but show a less favourable contraction on non-equidistant grids such as Radau-IIa points. We interprete SDC methods as fixed point iterations for the collocation system and propose new DIRK-type sweeps for stiff problems based on purely linear algebraic considerations. Good convergence is recovered also on non-equidistant grids. The properties of different variants are explored on a couple of numerical examples. © 2014 Springer Science+Business Media Dordrecht

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