„… . Fig. 1: Crash situation The integration of additional large-area crash levels with no hard …” „… FE software LS-Dyna® with Ultrasim®, a software tool developed by BASF for numerical mapping of …” „… of thermoplastic materials all in a single numerical approach. These include variables such as …”

„… significantly to CO2 reduction, with integration keeping system costs low and reducing total weight. 6 …” „… integration Styling-neutral design Minimization of costs, investment, weight, development costs and also …” „… standardization and functional integration. Functional integration is usually the initial driver here for …”

„… . Design of lightweight components occasionally involves part replacement, tooling, function integration …” „… part design and can improve it in every phase of its development. An appropriate numerical material …” „… reasonable numerical costs is a key element of the Simulation Strategy. Based on the direction-dependent …”

„… . Balmann, and R. Guardani. Modeling electrodialysis and photochemical process for their integration in …” „… Molecular Modeling, 13(10): 1039 1046, 2007. K. E. Brenan, S. L. Campbell, and L. R. Petzold. Numerical …” „… . Schittkowski, H. Pesch, and K. Sundmacher. Index analysis and numerical solution of a large scale nonlinear …”

„… the semi-discretization of the PDAE in the spatial coordinates and the numerical integration of the …” „… main e ort in the numerical treatment of the model is the integration of the semi-discretized and …” „… nitions of index are introduced and evaluated as a concept to support the modeling process, the numerical …”

„… explain numerous di culties observed in the context of the numerical solution of ionic mass transfer …” „… and an e cient numerical treatment with standard methods. The detailed transport models developed in …” „… economic performance of industrial ED processes would be the integration of the experiments with the …”

„… 1 Introduction This thesis is concerned with the integration of a model-based and experimental …” „… of the dynamic process behavior in transient experiments, as well as the e cient integration of …” „… numerical treatment of the dynamic model with generic methods. However, a major limitation of the method is …”

„… . Section 1.3.1). The integration of the hydrodynamic studies with a rigorous description of the ionic mass …” „… mathematical models and appropriate numerical methods for the integrated description of the complex …” „… transport in the framework of the LBM. Brie y, the LBM corresponds to an e cient numerical scheme for the …”

„… systematically derived in Chapter 4. The speci cation of these models and their integration in the hierarchical …” „… the x3-coordinate is formally obtained by integration of the models and the introduction of …” „… in a commercial modeling environment and does not require tailored numerical methods. By this means …”

„… 5 Numerical investigations In order to study the applicability of the proposed numerical methods …” „… , the numerical methods are investigated with respect to their performance in cardiovascular FSI …” „… the corresponding numerical methods introduced in Chapter 4 are investigated. The purpose of the …”

„… 4 Numerical methods In the previous chapter, several models were proposed for the investigation of …” „… of the models have to be solved approximately using numerical methods. In general, the unknown state …” „… building blocks as well as software tools for the data transfer from one 69 4 Numerical methods solver to …”

„… Bibliography [1] L. Achaba, M. Mahfouda, and S. Benhadida. “Numerical study of the non- Newtonian …” „… recirculation”. In: Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics …” „… : Physiological Reviews 91.1 (2011), pp. 327–387. [42] J. Chung and G. M. Hulbert. “Time integration algorithm for …”

„… gratitude to my supervisor Prof. Düster. His expertise in a broad range of topics in the field of numerical …” „… . . . . . . . . . . . . . . . . . . . . . 64 V Contents 3.3.7 Hemodynamic quantities . . . . . . . . . . . . . . . . 66 4 Numerical methods 69 …” „… 4.4.4 Field solver manipulation . . . . . . . . . . . . . . . 147 5 Numerical investigations 153 5.1 …”

„… simulation approach for cardiovascular FSI are introduced in this chapter. In the next chapter, numerical …” „… , te] and for all p ∈ [1, 2, . . . , np] 3.1.1 Solution approaches In view of the numerical methods to …” „… letters, while continuous variables or fields are represented using italic letters. The applied numerical …”

„… constitutes the target application for which the numerical methods in this work were developed. Accordingly …” „… study case can still give an impression of the use of numerical simulations in surgical planning and …” „… terms of the flow, which is evaluated from the velocity by integration over the boundary. The fluid and …”

„… numerical integration tools. 2. Analysed gear geometries and loading conditions The analyses were carried …” „… can be solved using a suitable numerical integration method and used to define the flash temperature …” „… periods, where a quasi-steady thermal state is achieved. The method consists of a preliminary numerical …”

„… the numerical errors introduced by direct collocation between tooth contacts and sub-structured gear …” „… contact conditions between the mating teeth and also avoids numerical artefacts in tooth load …” „… to avoid numerical errors leading to numerical spikes in tooth load distributions arising from …”

„… dynamic mesh forces are computed and analyzed. Finally, comparisons with the Runge-Kutta time integration …” „… integration scheme In order to evaluate the iterative spectral method efficiency, we performed comparisons …” „… with results obtained by integration time schemes. Among the many methods of temporal integration, we …”

„… obtained by a numerical time integration method called fourth Runge–Kutta method [9]. In order to get …” „… accurate results, the time step of numerical time integration method is set as 10-6. In this study, dynamic …” „… gear coupling by numerical analysis [3]. Barone proposed a finite element method to investigate the …”

„… article characterizes its core tribological features in a combined experimental and numerical approach …” „… on regression of numerical and experimental results. (1) Therein, U and W are dimensionless speed …” „… and load parameters respectively. SRR refers to the slide-to-roll ratio. Numerical results of …”

„… Castaneda [9] proposed a methodology for the numerical integration of the elastic-plastic constitutive …” „… , Springer Netherlands [9] Aravas N., P. C. P., Numerical methods for porous metals with deformation-induced …”

„… the two crossed helical gears can be considered. This serves for the numerical calculation of the …” „… .; STEMPLINGER, J.-P.; OTTO, M.; STAHL, K: Integration der Schraubradgetriebe in die FVA-Workbench …”

„… reduced in complexity to meet the real-time requirements. Comparison of numerical methods for real-time …” „… numerical solution methods can be optimised to speed up the calculation. Examples of this are the conversion …” „… inline integration [9]. On the other hand, model reduction can reduce the number of degrees of freedom …”