On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints

We present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints.

Super-resolution for doubly-dispersive channel estimation

In this work we consider the problem of identification and reconstruction of doubly-dispersive channel operators which are given by finite linear combinations of time-frequency shifts. Such operators arise as time-varying linear systems for example in radar and wireless communications. In particular, for information transmission in highly non-stationary environments the channel needs to be estimated quickly with identification signals of short duration and for vehicular application simultaneous high-resolution radar is desired as well. We consider the time-continuous setting and prove an exact resampling reformulation of the involved channel operator when applied to a trigonometric polynomial as identifier in terms of sparse linear combinations of real-valued atoms. Motivated by recent works of Heckel et al. we present an exact approach for off-the-grid super-resolution which allows to perform the identification with realizable signals having compact support. Then we show how an alternating descent conditional gradient algorithm can be adapted to solve the reformulated problem. Numerical examples demonstrate the performance of this algorithm, in particular in comparison with a simple adaptive grid refinement strategy and an orthogonal matching pursuit algorithm.

Performance Analysis of FEM Solvers on Practical Electromagnetic Problems

The paper presents a comparative analysis of different commercial and academic software. The comparison aims to examine how the integrated adaptive grid refinement methodologies can deal with challenging, electromagnetic-field related problems. For this comparison, two bench-mark problems were examined in the paper. The first example is a solution of an L-shape domain like test problem, which has a singularity at a certain point in the geometry. The second problem is an induction heated aluminum rod, which accurate solution needs to solve non-linear, coupled physical fields. The accurate solution of this problem requires applying adaptive mesh generation strategies or applying a very fine mesh in the electromagnetic domain, which can significantly increase the computational complexity. The results show that the fully-hp adaptive meshing strategies, which are integrated into Agros Suite, can significantly reduce the task's computational complexity compared to the automatic h-adaptivity, which is part of the examined, popular commercial solvers.

High performance Wannier interpolation of Berry curvature and related quantities with WannierBerri code

Wannier interpolation is a powerful tool for performing Brillouin zone integrals over dense grids ofkpoints, which are essential to evaluate such quantities as the intrinsic anomalous Hall conductivity or Boltzmann transport coefficients. However, more complex physical problems and materials create harder numerical challenges, and computations with the existing codes become very expensive, which often prevents reaching the desired accuracy. In this article, I present a series of methods that boost the speed of Wannier interpolation by several orders of magnitude. They include a combination of fast and slow Fourier transforms, explicit use of symmetries, and recursive adaptive grid refinement among others. The proposed methodology has been implemented in the python code WannierBerri, which also aims to serve as a convenient platform for the future development of interpolation schemes for other phenomena.

Spiral Tool Path Generation for CNC Machining Using Cloud of Points

This paper presents a new method to generate an adaptive spiral tool path for 3-axis CNC machining of the complex freeform surface directly from its representation in the form of the point cloud. The algorithm first constructs the uniform 2D circular mesh-grid to compute the Z (CL) points by applying the tool inverse offset method (IOM). Adaptive grid refinement is carried out iteratively until the surface form errors converge below the prescribed tolerance limits in both circumferential (forward) and radial (step) directions. Adaptive CL points are further refined to minimize the no. of tool lifts and generate an optimum sequence of machining regions. The optimized CL points are post-processed to generate the final CNC part programs in the ISO format. The part programs generated by our algorithm were extensively tested for various case studies using the commercial CNC simulator. The results were compared with those from the commercial CAM software. Our system was found to generate more efficient tool paths in terms of enhanced productivity, part quality, and reduced memory requirement.

Prediction of burning velocity and quenching distance of hydrogen flames

Atmospheric, laminar, stoichiometric, premixed hydrogen-air flames in a diverging channel are investigated by means of Computational Fluid Dynamics. This configuration has been recently used in a series of experimental investigations to determine the burning velocities and quenching distances for premixed flames of different fuels. The purpose of the present investigation is the validation of the prediction procedures for the burning speeds and quenching distances for hydrogen flames by comparing them with these measurements. Global and detailed reaction mechanisms are applied to describe the combustion process. For assuring an adequately fine resolution of the flame fronts, adaptive grid refinement techniques are applied. A reasonable agreement is observed with the experiments, where the detailed and global mechanisms are slightly overpredicting and underpredicting the quenching distance, respectively.