Application and modification of the POD method and the POD-DEIM for model reduction in porous-media simulations

Researchers with a continuum-mechanical background typically use a multi-phasic and multi-component modelling approach for materials with a saturated porous microstructure. Therefore, the mechanical behaviour is considered in a continuum-mechanical manner and solved using the finite-element method (FEM). The developed models need to be complex enough to capture the relevant properties of the considered materials, what often results in expensive simulations with a very large number of degrees of freedom (DOF). The aim of the present contribution is to reduce the computing time of these simulations through model-reduction methods, while the accuracy of the solution needs to be maintained. Therefore, the method of proper-orthogonal decomposition (POD) for linear problems and the discrete-empirical-interpolation method (DEIM) in combination with the POD method (POD-DEIM) for nonlinear problems are investigated. Using the POD method, a given data set is approximated with a low-dimensional subspace. To generate this data set, the vector of unknowns of the FE simulation is stored in a pre-computation in the full (unreduced) system in each time-step (so-called “snapshots” of the system). Dealing with porous-media problems, the primary variables are the solid displacement, the pore pressure and, depending on the particular problem, other primary variables. Following this, the primary variables have entries with very huge differences in their absolute values. As a result, non-negligible rounding errors may occur when applying the POD method. To overcome this problems, modifications of the classical POD method need to be performed for such problems. The present contribution discusses this issue and presents results for the reduced simulations of porous media. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel solution of volume-coupled multi-field problems using an Abaqus-PANDAS software interface

Numerical simulations have proven to be a powerful tool in several engineering disciplines, such as mechanical, civil and biomechanical engineering, and are thus widely used. However, the reliability of the simulations strongly relies on the governing material model. These models are usually developed in academic or industrial research projects and are implemented into dedicated software packages to proof their concepts. A transfer of these models from the research into a production-related environment is often time consuming and prone to failures, and therefore a costly task. The present work introduces a general interface between the research code PANDAS, which is a dedicated multi-field finite-element solver based on a monolithic solution strategy, and the commercial finite-element package Abaqus. The coupling is based on the user-defined element subroutine (UEL) of Abaqus. This procedure, on the one hand, allows for a straight-forward embedding of the PANDAS material models into Abaqus. On the other hand, it provides, in comparison to the native UEL subroutine of Abaqus, a user-friendly programming environment for user-defined material models with an extended number of degrees of freedom. Furthermore, the coupling also supports the parallel-analysis capabilities for large-scale problems on high-performance computing clusters. The Abaqus-PANDAS linkage can be applied to various coupled multi-field problems. However, the present contribution addresses, in particular, volume-coupled multi-field problems as they arise when proceeding from the Theory of Porous Media (TPM) as a modelling framework. For instance, it can be used to model partially or fully saturated soils, or chemically or electro-chemically driven swelling phenomena as they appear, for example, within hydrogels. Additionally, discontinuities, such as cracks, can be described for instance via phase-field models or by the extended finite-element method (XFEM). (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Advanced control and modeling of deposition processes

During the last decade, striking improvements could be achieved for the precise control of deposition processes in optical coating technology. For example, as a consequence of enormous progresses in measure- ment and computer technology, direct optical monitoring in a broad spectral range can be considered as a common tool in many production environments nowadays. Besides the development of the corresponding hardware and measurement channels, advanced approaches for the evaluation of the acquired data and new multiple sensor monitoring strategies moved into the focus of modern research on the way towards de- terministic deposition techniques. In this context, also innovative concepts for the simulation of deposition processes to forecast the result for a specified coating design and automatic online correction algorithms gained of importance to reduce the risk of failure in coating production. The present contribution will be dedicated to selected aspects in this field, especially addressing broad band optical monitoring systems. A short review on examples for existing hardware configurations and software tools will be presented illus- trating the advantages of modern process control techniques. Novel approaches based on the modeling of thin film growth are discussed as an additional strategy to improve the predictability of coating processes.     

Model reduction of porous-media problems using proper orthogonal decomposition

In the context of finite-element simulations of porous media, computing time and numerical effort is an important issue because the number of degrees of freedom of such coupled problems can become very large. Following this, model reduction plays an important role. A broad variety of materials exhibit a porous microstructure. In order to evaluate the overall response of these materials, a macroscopic continuum-mechanical modelling approach is used. Therefore, the complex inner structure of porous media is regarded in a multi-phasic and multi-component manner by means of the well-founded Theory of Porous Media (TPM). The mechanical behaviour of porous media is solved using the Finite-Element Method (FEM). The basic idea of model reduction is to transform a high dimensional system, in terms of the system's degrees of freedom, to a low dimensional subspace to minimise the computational effort while maintaining the accuracy of the solution. The method of proper orthogonal decomposition (POD) can be seen as a method to approximate a given data set with a low dimensional subspace. Furthermore, the POD method is independent of the type of the model and can be used for nonlinear systems as well as for systems of second order. In several applications, such as consolidation problems of partially saturated soils, commonly occurring motion sequences can be found, which can be used as typical “snapshots” of the system. Therefore, the application of the POD method to the simulation of porous media is discussed in the present contribution. Investigated computations of a biphasic standard problem show that the POD method reduces the numerical effort to solve the linearised system of equations in each iteration step. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)