Several a posteriori indicators in the framework of local grid adaptation and large eddy simulation (LES) are evaluated. In LES indicators must be capable to bound not only the discretisation error, but also the modeling error. Moreover, the numerical method must be able to adapt the computational grid dynamically, as the regions requiring different resolution are not static. The performance of different indicators is evaluated in two flow configurations. It turns out that the classic residual based error indicator and the newly introduced heuristic indicator perform best.

Fluorescence loss in photobleaching (FLIP) is a modern microscopy method for visualization of transport processes in living cells. Although FLIP is widespread, an automated reliable analysis of image data is still lacking. This paper presents a framework for modeling and simulation of FLIP sequences as reaction---diffusion systems on segmented cell images. The cell geometry is extracted from microscopy images using the Chan---Vese active contours algorithm (IEEE Trans Image Process 10(2):266---277, 2001). The PDE model is subsequently solved by the automated Finite Element software package FEniCS (Logg et al. in Automated solution of differential equations by the finite element method. Springer, Heidelberg, 2012). The flexibility of FEniCS allows for spatially resolved reaction diffusion coefficients in two (or more) spatial dimensions.

We consider the problem of uncertainty quantification for extreme scale parameter dependent problems where an underlying low rank property of the parameter dependency is assumed. For this type of dependency the hierarchical Tucker format offers a suitable framework to approximate a given output function of the solutions of the parameter dependent problem from a number of samples that is linear in the number of parameters. In particular we can a posteriori compute the mean, variance or other interesting statistical quantities of interest. In the extreme scale setting it is already assumed that the underlying fixed-parameter problem is distributed and solved for in parallel. We provide in addition a parallel evaluation scheme for the sampling phase that allows us on the one hand to combine several solves and on the other hand parallelise the sampling.

We propose a new method for the solution of discretised elliptic PDE eigenvalue problems. The new method combines ideas of domain decomposition, as in the automated multi-level substructuring (short AMLS), with the concept of hierarchical matrices (short $$\fancyscript{H}$$H-matrices) in order to obtain a solver that scales almost optimal in the size of the discrete space. Whereas the AMLS method is very effective for PDEs posed in two dimensions, it is getting very expensive in the three-dimensional case, due to the fact that the interface coupling in the domain decomposition requires dense matrix operations. We resolve this problem by use of data-sparse hierarchical matrices. In addition to the discretisation error our new approach involves a projection error due to AMLS and an arithmetic error due to $$\fancyscript{H}$$H-matrix approximation. A suitable choice of parameters to balance these errors is investigated in examples.

Interest in renewable, green, and sustainable energy has risen sharply in recent years. The use of marine turbines to extract kinetic energy from the tidal current is gaining popularity. CFD modeling is carried out to investigate the surrounding flow behavior and thus develop effective marine turbine systems. However, visualizing the simulation results remains a challenging task for engineers. In this paper, we develop, explore and present customized visualization techniques in order to help engineers gain a fast overview and intuitive insight into the flow past the marine turbine. The system exploits multiple-coordinated information-assisted views of the CFD simulation data. Our application consists of a tabular histogram, velocity histogram, parallel coordinate plot, streamline plot and spatial views. Information-based streamline seeding is used to investigate the behavior of the flow deemed interesting to the engineer. Specialized, application-specific information based on swirling flow is derived and visualized in order to evaluate turbine blade design. To demonstrate the usage of our system, a selection of specialized case scenarios designed to answer the core questions brought out by engineers is described. We also report feedback on our system from CFD experts researching marine turbine simulations.

A version of the $${{\fancyscript{H}}} $$H-LU factorization is introduced, based on the individual computational tasks occurring during the block-wise $${{\fancyscript{H}}} $$H-LU factorization. The dependencies between these tasks form a directed acylic graph, which is used for efficient scheduling on parallel systems. The algorithm is especially suited for many-core processors and shows a much improved parallel scaling behavior compared to previous $${{\fancyscript{H}}} $$H-LU factorization algorithms.

The visualization of huge datasets may be required by a broad spectrum of scientific applications encompassing, among others, the medicine, chemistry, architecture and aero-space fields. Unfortunately, in some cases, visualization devices might be unable to locally store such data. Datasets could be either too large (thus requiring to be stored in dedicated data centers) or might need specialized hardware to be processed (like high performance computers or cloud computing architectures). Some applications could even prevent, e.g., for privacy and/or security issues, a data transfer from data centers to (client) visualization devices. Under these circumstances, only representations of data, rather than data themselves, could be sent to the client side. Remote visualization has been often regarded as an interesting solution to the above problems, as data can be remotely processed where resources are available and only their representations are to be managed by the visualization devices. Although with the remote visualization paradigm it can be possible to minimize the resources required on the client side, it might also involve several issues basically related to the underlying network channel. In fact, network bandwidth, latency and interactive frame rates are the main parameters to be taken into account when data processing and data visualization are two logically and physically separated processes. A lot of work is known in the literature mainly related to the reduction of the network load from data centers to client devices. Compression scheme have been used to reduce the amount of data to be transmitted, both considering flows of

Interactions of nanoparticles with respiratory fluids such as airway mucus are currently under investigation and are involved in a variety of applications. The clearance processes of those nanoparticles are still not fully understood. This study presents an approach to describe deposition, sedimentation and clearance of nanoparticles within mucus with numerical and analytical models: Particle deposition as well as motility, sedimentation and clearance were simulated with Computational Fluid Dynamics (CFD) and described analytically. Furthermore mucus plasticity as pathway for complex particle translocation was simulated using grid-free CFD methods. We could demonstrate that fluid dynamics strongly influence the fate of deposited nanoparticles in mucus: Sedimentation, impaction and diffusion were shown to be unlikely to contribute to particle translocation. However, intrinsic plasticity of mucus slabs and collision of such slabs may enhance particle translocation towards the pulmonary epithelium.

This work addresses an optimal control approach for a model problem in cardiac electrophysiology with the goal of extinction of a reentry phenomenon. After the introduction of the mathematical model, the derivation of the optimality system, the description of its discretization and a numerical feasibility study in a parallel environment are provided.

In this paper we consider multigrid methods for solving saddle point problems. The choice of an appropriate smoothing strategy is a key issue in this case. Here we focus on the widely used class of collective point smoothers. These methods are constructed by a point-wise grouping of the unknowns leading to, e.g., collective Richardson, Jacobi or Gauss-Seidel relaxation methods. Their smoothing properties are well-understood for scalar problems in the symmetric and positive definite case. In this work the analysis of these methods is extended to a special class of saddle point problems, namely to the optimality system of optimal control problems. For elliptic distributed control problems we show that the convergence rates of multigrid methods with collective point smoothers are bounded independent of the grid size and the regularization (or cost) parameter.