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IRTG Modern Inverse Problems (MIP)

Kategorie: ‘Research Topics’

Modeling and Simulation of Solidification with Isogeometric Interface Tracking Methods

09. Oktober 2018 | von

Prof. Dr. Stefanie Egleti

The proposed project originates in the field of production engineering—or more specifically—primary manufacturing processes. The underlying principles of these processes is that material is brought into a liquid state in order to make it shapable. This shape is then sought to be maintained throughout a subsequent solidification process, which returns the material to a solid state and makes the product usable under standard environmental conditions. The state of the material—here liquid or solid—depends on process conditions, such as temperature, pressure, etc. The transition from a liquid to a solid phase—the solidification—is a spontaneous process initiated by heat extraction (cooling). The process is locally initiated by nucleation and proceeds by movement of phase boundaries. During solidification, shrinkage and warpage may occur, leading to negative effects on the final product’s quality. In order to gain a better understanding of these effects, this project focuses on modeling and simulation of the solidification process. It covers the following aims:

Aim 1: Derivation of a nucleation model as well as definition of a tracking method for the phase interface within an isogeometric context;

Aim 2: Evaluation of properties resulting from solidification—examples are shrinkage, warpage, residual stresses—that are relevant to engineering applications.

Within the project, semi-crystalline polymers in an injection molding process will serve as a working example.

Model-Based Generation of Linear Algebra Software

09. Oktober 2018 | von

Prof. Paolo Bientinesi, Ph.D.

This project tackles the automatic optimization of linear algebra operations that represent the computational bottleneck in scientific simulations and in data analyses.

The PI’s have extensive experience in parallel computing and in the development of linear algebra kernels, as well as performance models and automation; the combined expertise will make it possible to streamline the generation of high-performance algorithms and code, tailored towards specific applications, and targeting existing and upcoming computing architectures. The methodology builds on stochastic performance models, and formal derivation methods, and will be applied to selected operations, such as those arising in global optimization.
Concisely, the project has three intertwined aims.

Aim 1: Identification and development of a set of high-performance low-level kernels, sufficient to support the set of target operations.

Aim 2: Derivation of performance and scalability models for the building blocks, with quantification of the associated uncertainties.

Aim 3: “Performance model”-based decomposition of high-level operations in terms of the available building blocks.

In sharp contrast to the typical library development, our approach follows a reverse order, akin to an inverse problem: Given a target known functionality, the objective is to identify the composition of kernels that minimizes a cost function.

Computational Tools for Chemical Imaging

09. Oktober 2018 | von

Prof. Benjamin Berkels

The project will advance the state of the art in segmentation and unximing of data from chemical imaging, which is an umbrella term for image acquisition techniques that record a full spectral band of data at each pixel. A major challenge for the analysis of hyperspectral data is its huge size and high dimensionality.

Segmentation of hyperspectral data is the task of partitioning the image domain into disjoint sub-regions based on a suitable notion of spectral homogeneity, i.e. assigning a class label to each pixel based on its spectral vector data. For instance, for hyperspectral satellite images, such classes could be soil, water, grass, street, etc. A more general task than segmentation is called unmixing. Instead of belonging to just one class, unmixing considers each pixel to be a mixture of a number of constituents. Unmixing then needs to determine both the mixture ratios and the constituents. Nowadays, numerous hyperspectral image modalities are available, which makes this research relevant for a wide range of applications. One considered application will be cancer treatment, where Fourier transform infrared spectroscopy data of human tissue samples needs to be classified into classes like “highly cancerous”, “mildly cancerous” or “normal”.

The main aims of this project are:
• Robust segmentation of hyperspectral data with large intra-class variation;
• Unmixing of mixture of  mixtures data using hierarchical matrix factorization.

Novel Stabilized Finite-Element Methods for Microstructured and Complex Fluids

08. Oktober 2018 | von

Prof. Marek Behr, Ph.D.

The project will advance the state of the art in the computational treatment of viscoelastic (VE) constitutive equations and similar model equations arising elsewhere. The applications of this research range from production engineering and melt-based forming processes (die swell of VE fluid shown in figure), to biomedical device design, to aerospace technology.

Low-order stabilized finite elements (FEM) are the workhorse of computational engineering, but are sensi- tive to element quality and stabilization parameters. Discontinuous Petrov-Galerkin (DPG) methods have a solid mathematical foundation and robustness, but are not yet used in industrial contexts. By merging the properties of FEM and DPG, robust method for microstructured fluids in industrial settings will be obtained.

The research goals of this project are:

  • Understanding of the stability and accuracy properties of two alternate finite element dis- cretization approaches;

  • Transfer of Discontinuous Petrov-Galerkin stability and accuracy advantages to low-order industrial FE formulations;

  • Insight into numerical behavior of sensitivities and adjoints required for design tasks in both approaches.