2016, Mihaljević-Brandt, Helena, Santamaría, Lucía, Tullney, Marco

Despite the increasing number of women graduating in mathematics, a systemic gender imbalance persists and is signified by a pronounced gender gap in the distribution of active researchers and professors. Especially at the level of university faculty, women mathematicians continue being drastically underrepresented, decades after the first affirmative action measures have been put into place. A solid publication record is of paramount importance for securing permanent positions. Thus, the question arises whether the publication patterns of men and women mathematicians differ in a significant way. Making use of the zbMATH database, one of the most comprehensive metadata sources on mathematical publications, we analyze the scholarly output of ∼150,000 mathematicians from the past four decades whose gender we algorithmically inferred. We focus on development over time, collaboration through coautorships, presumed journal quality and distribution of research topics—factors known to have a strong impact on job perspectives. We report significant differences between genders which may put women at a disadvantage when pursuing an academic career in mathematics.

2013, Si, Hang

TetGen is a software for tetrahedral mesh generation. Its goal is to generate good quality tetrahedral meshes suitable for numerical methods and scientific computing. It can be used as either a standalone program or a library component integrated in other software. The purpose of this document is to give a brief explanation of the kind of tetrahedralizations and meshing problems handled by TetGen and to give a fairly detailed documentation about the usage of the program. Readers will learn how to create tetrahedral meshes using input files from the command line. Furthermore, the programming interface for calling TetGen from other programs is explained.

2017, Redmann, Martin

When solving linear stochastic partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce computational complexity. A particular MOR technique to obtain a reduced order model (ROM) is singular perturbation approximation (SPA), a method which has been extensively studied for deterministic systems. As so-called type I SPA it has already been extended to stochastic equations. We provide an alternative generalisation of the deterministic setting to linear systems with Lévy noise which is called type II SPA. It turns out that the ROM from applying type II SPA has better properties than the one of using type I SPA. In this paper, we provide new energy interpretations for stochastic reachability Gramians, show the preservation of mean square stability in the ROM by type II SPA and prove two different error bounds for type II SPA when applied to Lévy driven systems.

2013, Parameswaran, A.J., Tibar, M.

We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X.

2016, Blyuss, Konstantin B., Manchanda, Ranjit, Kurths, Jürgen, Alsaedi, Ahmed, Zaikin, Alexey

Editorial

2016, Borchardt, Jürgen, Mathé, Peter, Printsypar, Galina

The WIAS software package BOP is used to simulate gas turbine models. In order to make accurate predictions the underlying models need to be calibrated. This study compares different strategies of model calibration. These are the deterministic optimization tools as nonlinear least squares (MSO) and the sparsity promoting variant LASSO, but also the probabilistic (Bayesian) calibration. The latter allows for the quantification of the inherent uncertainty, and it gives rise to a surrogate uncertainty measure in the MSO tool. The implementation details are accompanied with a numerical case study, which highlights the advantages and drawbacks of each of the proposed calibration methods.

2017, Goyal, Pawan, Redmann, Martin

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems and hence reduce computational complexity. A particular class of MOR techniques are H2-optimal methods such as the iterative rational Krylov subspace algorithm (IRKA) and related schemes. However, these methods are used to obtain good approximations on a infinite time-horizon. Thus, in this work, our main goal is to discuss MOR schemes for time-limited linear systems. For this, we propose an alternative time-limited H2-norm and show its connection with the time-limited Gramians. We then provide first-order optimality conditions for an optimal reduced order model (ROM) with respect to the time-limited H2-norm. Based on these optimality conditions, we propose an iterative scheme which upon convergences aims at satisfying these conditions. Then, we analyze how far away the obtained ROM is from satisfying the optimality conditions.We test the efficiency of the proposed iterative scheme using various numerical examples and illustrate that the newly proposed iterative method can lead to a better reduced-order compared to unrestricted IRKA in the time interval of interest.

2016, Radziunas, Mindaugas

This report summarizes our scientific activities within the project MANUMIEL (BMBF Program “Förderung der Wissenschaftlich-Technologischen Zusammenarbeit (WTZ) mit der Republik Moldau”, FKZ 01DK13020A). Namely, we discuss modeling of external cavity diode lasers, numerical simulations and analysis of these devices using the software package LDSL-tool, as well as the development of this software.

2013, Hömberg, Dietmar, Petzold, Thomas, Rocca, Elisabetta

We study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of the Maxwells equations coupled with an internal energy balance and an ODE for the volume fraction of austenite, the high temperature phase in steel. We first solve the initial boundary value problem associated by means of a Schauder fixed point argument coupled with suitable a-priori estimates and regularity results. Moreover, we prove a stability estimate entailing, in particular, uniqueness of solutions for our Cauchy problem. We conclude with some finite element simulations for the coupled system.

2015, Huang, Weizhang, Kamenski, Lennard, Si, Hang

We study a mesh smoothing algorithm based on the moving mesh PDE (MMPDE) method. For the MMPDE itself, we employ a simple and efficient direct geometric discretization of the underlying meshing functional on simplicial meshes. The nodal mesh velocities can be expressed in a simple, analytical matrix form, which makes the implementation of the method relatively easy and simple. Numerical examples are provided.