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This thesis is concerned with linear and non-linear optimal flow control problems which are modeled by systems of partial differential equations. The numerical treatment of such problems, especially in the context of flow problems, is often very expensive and challenging. To tackle this complexity, we present parallel approaches based on non-overlapping domain decomposition methods that exploit the computational power provided by modern high performance computing technologies.

We model, simulate and calculate breathing and particle depositions in the human lungs. We review the theory and discretization of fluid mechanics, the anatomy, physiology and measuring methods of lungs. A new model is introduced and investigated with a sensitivity analysis using the singular value decomposition. Particle depositions are simulated in patient-specific and schematized human lungs and compared to the particle deposition in a multiplicative model of subsequent bifurcations.

Asynchronous methods minimize idle times by removing synchronization barriers, and therefore allow the efficient usage of computer systems. The implied high tolerance with respect to communication latencies improves the fault tolerance. As asynchronous methods also enable the usage of the power and energy saving mechanisms provided by the hardware, they are suitable candidates for the highly parallel and heterogeneous hardware platforms that are expected for the near future.

In dieser Arbeit wird beschrieben, wie ein Modellparameter einer instationären partiellen Differentialgleichung mit der Maximum-Likelihood-Methode geschätzt werden kann und wie die Zuverlässigkeit bei einer solchen Schätzung durch Bestimmung eines D-optimalen Designs maximiert werden kann. Diesbezüglich wird die Fisher-Informationsmatrix verwendet. Am Beispiel eines Säulenchromatographieprozesses werden die in dieser Arbeit beschriebenen Optimierungsverfahren numerisch umgesetzt.

This thesis is concerned with the application of hp-adaptive finite element methods to a mathematical model of immiscible two-component flows. With the aim of simulating the flow processes in microfluidic optical devices based on liquid-liquid interfaces, we couple the time-dependent incompressible Navier-Stokes equations with a level set method to describe the flow of the fluids and the evolution of the interface between them.

In this work, we evaluate different solvers and preconditioners for solving the barotropic system of an ocean model to achieve optimal performance on a high-performance computer. In the field of support theory, we derive upper bounds for the condition number of a system that is preconditioned with a block-Jacobi Steiner graph preconditioner. Furthermore, we analyze the application of a high-level approach for programming preconditioners on FPGAs.

In this work we examine two kinds of applications in terms of stability and perform numerical evaluations and benchmarks on parallel platforms. We consider the applicability of pseudospectra in the field of hydrodynamic stability to obtain more information than a traditional linear stability analysis can provide. Furthermore, we treat the neutron transport criticality problem and highlight the Davidson method as an attractive alternative to the so far widely used power method in that context.

The thesis is concerned with the study of methods in high-performance computing for simulation and optimisation of flow problems that occur in the framework of microflows. We consider the adequate use of techniques in parallel computing by means of finite element based solvers for partial differential equations and by means of sensitivity- and adjoint-based optimisation methods. The main focus is on three-dimensional, low Reynolds number flows described by the instationary Navier-Stokes equations.

An overall strategy for numerical simulations of the full human respiratory system is introduced. The integrative approach takes advantage of numerical simulation, high performance computing and newly developed mathematical optimisation techniques, all based on a mesoscopic model description and on lattice Boltzmann methods as discretisation strategies. Validated numerical results are presented for the simulation of respirations in a real human lung and nose geometry captured by CT.