Jörg Wensch

Optimised coupling of hierarchies in image registration

Image registration algorithms rely on multilevel strategies in order to improve efficiency and robustness. Hierarchies in image resolution, the underlying grids for spline-based transformations, as well as the regularisation parameters are used. This paper deals with the optimisation of the coupling of these hierarchies. An image registration procedure - suitable for 2D polyacrylamide gel electrophoresis images - using piecewise bilinear transformations and an intensity based objective function with a regularisation term based on the elastic deformation energy is described. The resulting nonlinear least squares problem is solved by the Gauss-Newton method. Techniques reminiscent of dynamic programming are used to optimise the coupling of hierarchies in image and transformation resolution. Besides using these techniques to devise an advantageous fixed coupling of both hierarchies, we favour incorporating the dynamic programming ideas into the final registration algorithm. This leads to an adaptive and streamlined approach. Numerical experiments on 2D-PAGE images show that the adaptive registration algorithm is much more reliable than the same algorithm with a fixed coupling of hierarchies. The proposed optimisation procedure for the coupling of hierarchies presents a valuable tool to optimise other registration algorithms.

Computation of Thermo-Elastic Deformations on Machine Tools - A study of Numerical Methods

Modern machine tools are highly optimized with respect to their design and the production processes they are capable to. Now for further advances, especially a detailed knowledge about the thermo-elastic behavior is needed, because the nowadays still existing deficits are mainly related to this. That is why, endeavors in improvement, like the optimization of the design, the evaluation of new materials and the regulation of the production process, particularly rely on accurate computed thermal deformations. One possible approach to increase their quality is to also include the relevant structural variabilities of the machine tools as well as the resulting interactions between the coupled parts within the calculations. In this article, three different numerical methods are presented, which include structural motions in thermo-elastic analyses. Thereby, several conflicting criteria, like real-time capability, memory saving issues and accuracy are fulfilled each time in a different manner. Those methods are afterwards compared with respect to their runtime and accuracy. Finally, the paper concludes with a classification of the usability of the methods in real-time control and optimization tasks.

Towards utilizing repeating structures for constant time compilation of large Modelica models

Modelica is a language for modeling and simulating complex physical systems. A Modelica compiler generates a differential-algebraic equation (DAE) system from Modelica source code. The physical system is simulated by solving the DAE numerically. Before this can be done, the Pantelides algorithm is often applied to reduce the index of the DAE. Modelicas ability of structured programming makes it easy to describe physical systems with a repeating structure, like a roller chain, a battery pack or a solar panel. Such Modelica models generate DAE systems with many repeated sections. The Pantelides algorithm is not capable of using and preserving these repeating structures. As a consequence Modelica compilers need to unroll such structures. Huge memory consumption and the generation of bulky source code for the numerical solver is often a consequence. This article discusses techniques, which make it possible to preserve and use repeating structures during Pantelides index reduction. It is shown how the search for augmenting paths and the calculation of minimal structural singular subsets can be shortened. The method is restricted to repetitions, which are described by non-nested for-loops.

A General Method to Validate Breeding Value Prediction Software

The validity of national genetic evaluations depends on the quality of input data, on the model of analysis, and on the correctness of genetic evaluation software. A general strategy was developed to validate national breeding value prediction software: performances from a real data file were replaced with simulated ones, created from simulated fixed and random effects and residuals in such a way that BLUP estimates from the evaluation software must be equal to the simulated effects. This approach was implemented for a multiple-trait model and a random regression test-day model. An example was presented on test-day observations analyzed with a random regression animal model including a lactation curve described as a sum of fixed polynomial regression and fixed spline regression on days in milk, and with genetic and permanent environmental effects modeled by using Legendre polynomials of order 2. Residuals had heterogeneous variances, and phantom parent groups were included. This method can be easily extended to other linear models. The comparison of genetic evaluation results with simulated true effects is used to demonstrate the great efficiency and usefulness of the proposed method.

Defect corrected averaging for highly oscillatory problems

The accurate solution of partial differential equations with highly oscillatory source terms over long time scales constitutes a challenging problem. There exists a variety of methods dealing with problems where there are processes, equations or variables on fine and coarse scales. Multiscale methods have in common, that they neither fully resolve the fine scale, nor completely ignore it. On the one hand, these methods strive, without significantly sacrificing accuracy or essential properties of the system, to be much more efficient than methods that fully resolve the fine scale. On the other hand, these methods should be considerably more accurate than methods that completely ignore the fine scale. Our defect corrected averaging procedure is based on a modified coarse scale problem, that approximates the solution of the fine scale problem in stroboscopic points. Nevertheless, our approximation process is clearly different from the stroboscopic averaging method. We give an error estimate for the solution of the modified problem. The computational efficiency of the approximation is furthermore improved by the application of preconditioning techniques. Tests on numerical examples show the efficiency and reliability of our approach.

High-Accuracy Thermo-Elastic Simulation on Massively Parallel Computer

Subproject A07 develops and explores numerical methods and techniques to implement them to solve problems in connection with thermo-elastic subassemblies’ and machine tools’ simulation in the CRC/Transregio 96. For this purpose, high-resolution discretization methods were developed, tested and applied both for high resolution discretization in space and for efficient integration in the long term.

A Parallel Communication Structure for the Multilayer Shallow Water Equations

We propose a horizontal discretization of the multilayer shallow water equations by the Hamiltonian particle mesh method. The equations of motion are derived by Hamiltons principle applied to the discrete energies. The structure of the particle mesh method allows a convenient parallelization. There is no communication between particles in different layers, only the data on the Eulerian mesh have to be communicated. A straightforward parallelization results in a broadcast of all layer heights. This is circumvented by a butterfly‐type communication structure to keep communication at O (logN), N being the number of layers.

Generic C++ Implementation of High-Performance BFS-RBF-based Mesh Motion Schemes

Multi‐Dimensional fluid‐ and structural dynamics problems are solved by computational methods based on Arbitrary Lagrange Euler (ALE) formulation of the continuum mechanical conservation equations. The paper presents a new modification of the radial basis function (RBF) based mesh motion scheme, which combines the RBF interpolation with the breadth‐first search (BFS) algorithm. In this emerging domain, it is still unknown which algorithmic approach is the most suitable. Therefore, we realized our C++ implementation on a high abstraction level enabling broad customization and easy extension for further algorithmic research without sacrificing performance.

Multirate Time Integration for Compressible Atmospheric Flow

We generalise split‐explicit Runge‐Kutta methods utilised in atmospheric dynamics simulation where fast sub‐processes (sound waves) are integrated by small time steps. The inclusion of fixed tendencies of previous stages leads to an improvement of the stability barrier for the acoustics equation by a factor of two. Order and stability analysis is based on the assumption of exact integration of fast subprocesses.