@misc{KlapprothSchielaDeuflhard2009, author = {Klapproth, Corinna and Schiela, Anton and Deuflhard, Peter}, title = {Consistency Results for the Contact-Stabilized Newmark Method}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11164}, number = {09-06}, year = {2009}, abstract = {The paper considers the time integration of frictionless dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Among the numerical integrators, interest focuses on the contact-stabilized Newmark method recently suggested by Deuflhard et al., which is compared to the classical Newmark method and an improved energy dissipative version due to Kane et al. In the absence of contact, any such variant is equivalent to the St{\"o}rmer-Verlet scheme, which is well-known to have consistency order 2. In the presence of contact, however, the classical approach to discretization errors would not show consistency at all because of the discontinuity at the contact. Surprisingly, the question of consistency in the constrained situation has not been solved yet. The present paper fills this gap by means of a novel proof technique using specific norms based on earlier perturbation results due to the authors. The corresponding estimation of the local discretization error requires the bounded total variation of the solution. The results have consequences for the construction of an adaptive timestep control, which will be worked out subsequently in a forthcoming paper.}, language = {en} } @misc{Weiser2009, author = {Weiser, Martin}, title = {On goal-oriented adaptivity for elliptic optimal control problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11192}, number = {09-08}, year = {2009}, abstract = {The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of interest. Finally, the efficiency of the error estimator and generated meshes are demonstrated on numerical examples.}, language = {en} } @misc{SchielaWeiser2009, author = {Schiela, Anton and Weiser, Martin}, title = {Barrier methods for a control problem from hyperthermia treatment planning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11567}, number = {09-36}, year = {2009}, abstract = {We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.}, language = {en} } @phdthesis{Zschiedrich2009, author = {Zschiedrich, Lin}, title = {Transparent boundary conditions for Maxwell's equations: Numerical concepts beyond the PML method}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000013994-8}, year = {2009}, abstract = {Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term "multiply structured exterior domain" is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well.}, language = {en} } @phdthesis{Roeblitz2009, author = {R{\"o}blitz, Susanna}, title = {Statistical Error Estimation and Grid-free Hierarchical Refinement in Conformation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000008079-9}, year = {2009}, abstract = {The understanding of geometric structures and dynamical properties of molecular conformations gives insight into molecular long-term behavior. The identification of metastable conformations together with their life times and transition patterns is the intention of conformation dynamics. Conformation dynamics is a multi-scale approach that leads to a reduced description of the dynamical system in terms of a stochastic transition probability matrix. The present thesis deals with the error analysis of computed matrices and the resulting matrix functions. Since conformational membership vectors, as they are computed by the Robust Perron Cluster Analysis (PCCA+), form an invariant subspace of the transition matrix, subspace-based error estimators are of particular interest. The decomposition of the state space into basis functions and the approximation of integrals by Monte-Carlo quadrature give rise to row-wise correlated random matrices, for which stochastic norms are computed. Together with an appropriate statistical model for the distribution of matrix rows, this allows for the calculation of error bounds and error distributions of the invariant subspace and other variables of interest. Equilibration of errors among the basis functions can be achieved by enhanced sampling in regions where the trajectories are mixing slowly. Hierarchical refinement of such basis functions systematically improves the clustering into metastable conformations by reducing the error in the corresponding invariant subspace. These techniques allow for an evaluation of simulation results and pave the way for the analysis of larger molecules. Moreover, the extension of PCCA+ to non-reversible Markov chains, verified by the corresponding perturbation theory, and the modification of the objective function for the case of soft membership vectors represent a further generalization of the clustering method, thus continuing the development from PCCA over PCCA+ to PCCA++. The methods developed in this thesis are useful for but not limited to conformation dynamics. In fact, they are applicable to a broader class of problems which combine domain decomposition with Monte-Carlo quadrature. Possible application areas may include the chemical master equation or quantum dynamical systems.}, language = {en} } @misc{KilianMuench2009, author = {Kilian, Susanne and M{\"u}nch, Matthias}, title = {A new generalized domain decomposition strategy for the efficient parallel solution of the FDS-pressure equation. Part I: Theory, Concept and Implementation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11332}, number = {09-19}, year = {2009}, abstract = {A world-wide used program for the simulation of fire-induced flows is the Fire Dynamics Simulator (FDS) which originally was developed for a purely serial execution on single-processor computing systems. Due to steadily increasing problem sizes and accuracy requirements as well as restrictions in storage capacity and computing power on single-processor systems, the efficient simulation of the considered fire scenarios can only be achieved on modern high-performance systems based on multi-processor architectures. The transition to those systems requires the elaborate parallelization of the underlying numerical methods which must guarantee the same result for a given problem as the corresponding serial execution. Unfortunately, one fundamental serial serial solver of FDS, the pressure solver, only possesses a low degree of inherent parallelizm. Its current parallelization may cause additional numerical errors, casually leading to significant losses of accuracy or even numerical instabilities. In order to ensure that the parallelization errors are limited by the leading error of the numerical scheme such that second order convergence for the whole method can be acchieved, optimized parallelization concepts must be designed. With respect to these considerations this articles gives an overview of the current parallel pressure solver as well as the problems related to it and presents an alternative method, SCARC, to overcome the existing complicacies. Part I explains the theory, concept and implementation of this new strategy, whereas Part II describes a series of validation and verification tests to proof its correctness.}, language = {en} } @misc{MuenchKilian2009, author = {M{\"u}nch, Matthias and Kilian, Susanne}, title = {A new generalized domain decomposition strategy for the efficient parallel solution of the FDS-pressure equation. Part II: Verification and Validation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11340}, number = {09-20}, year = {2009}, abstract = {Because CFD programs, like FDS, generally consist of a large number of different components representing the variety of participating numerical algorithms and chemical / physical processes, it is nearly impossible to verify such codes in their entirety, for example with comparisons of fire tests. Instead, a careful verification and validation with respect to the underlying mathematical conditions and applied numerical schemes is indispensable. In particular, error cancelations between single program components can only be detected by such detailed component-level tests. In part I of this article series a conceptual deficiency of the FDS program package with regard to multi-mesh computations was illustrated and an alternative domain decomposition strategy FDS-ScaRC was introduced. In this second part we will present the structure of a comprehensive test concept and the needs for a more mathematically and numerically orientated test procedure that is much more suited for a reliable evaluation than only a simple visual comparison of the numerical results with experimental fire tests. After a general introduction of our test concept we will demonstrate the high potential of the new FDS-\scarc{} technique compared to the FDS-FFT technique which is used in the FDS program package as yet. Based on this concept, we will present a comprehensive set of analytical and numerical test results.}, language = {en} } @misc{RuprechtKleinMajda2009, author = {Ruprecht, Daniel and Klein, Rupert and Majda, Andrew J.}, title = {Moisture-Gravity Wave Interactions in a Multiscale Environment}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11358}, number = {09-21}, year = {2009}, abstract = {Starting from the conservation laws for mass, momentum and energy together with a three species, bulk microphysic model, a model for the interaction of internal gravity waves and deep convective hot towers is derived by using multiscale asymptotic techniques. From the resulting leading order equations, a closed model is obtained by applying weighted averages to the smallscale hot towers without requiring further closure approximations. The resulting model is an extension of the linear, anelastic equations, into which moisture enters as the area fraction of saturated regions on the microscale with two way coupling between the large and small scale. Moisture reduces the effective stability in the model and defines a potential temperature sourceterm related to the net effect of latent heat release or consumption by microscale up- and downdrafts. The dispersion relation and group velocity of the system is analyzed and moisture is found to have several effects: It reduces energy transport by waves, increases the vertical wavenumber but decreases the slope at which wave packets travel and it introduces a lower horizontal cutoff wavenumber, below which modes turn into evanescent. Further, moisture can cause critical layers. Numerical examples for steadystate and timedependent mountain waves are shown and the effects of moisture on these waves are investigated.}, language = {en} } @misc{Massing2009, type = {Master Thesis}, author = {Massing, Andr{\´e}}, title = {1D-Reduktion thermal signifikanter Aderstr{\"a}nge in der Hyperthermie-Modellierung}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11407}, school = {Zuse Institute Berlin (ZIB)}, year = {2009}, abstract = {In dieser Arbeit wird ein neuer Ansatz zur Modellierung von thermal signifikanten Gef{\"a}ßstr{\"a}ngen im Hyperthermie-Kontext betrachtet. Ausgehend von einer Konvektions-Diffusions-Gleichung wird durch Reskalierung des Massenflussterms eine Reduktion des Adergebietes auf eine 1D-Struktur erreicht. Nach numerischen Vorbetrachtungen wird die Grenzgleichung innerhalb einer verallgemeinerten Sobolev-Algebra formuliert. Die Untersuchung der L{\"o}sungsfamilie in klassischen Funktionenr{\"a}umen zeigt, dass deren schwacher Grenzwert die L{\"o}sung der korrespondierenden Diffusions-Gleichung ist. Die Diskretisierung einer formalen Grenzgleichung mit Linienstromanteil stellt jedoch eine gute Approximation an die Diskretisierung des urspr{\"u}nglichen Problems dar, wenn man die lokale Maschenweite an die Gef{\"a}ßradien koppelt und bei erh{\"o}htem Genauigkeitsbedarf auf ein vollst{\"a}ndiges 3D-Modell umschaltet.}, language = {de} } @misc{SchmidtOevermannBastiaansetal.2009, author = {Schmidt, Heiko and Oevermann, Michael and Bastiaans, Rob J.M. and Kerstein, Alan R.}, title = {A Priori Tabulation of Turbulent Flame Speeds via a Combination of a Stochastic Mixing Model and Flamelet Generated Manifolds, Extended to Incorporate Strain Effects}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11214}, number = {09-09}, year = {2009}, abstract = {In this paper we revisit the a priori turbulent flame speed tabulation (TFST) technique for a given parameter space within the region of flamelet combustion-regimes. It can be used as a subgrid-scale (SGS) model in Large Eddy Simulation (LES). In a first step, stationary laminar flamelets are computed and stored over the progress variable following the ideas of flamelet generated manifolds (FGM). In a second step, the incompressible one-dimensional Navier-Stokes equations supplemented by the equation for the progress variable are solved on a grid that resolves all turbulent scales. Additionally, turbulent transport is implemented via the linear eddy model (LEM). The turbulent flame structures are solved until a statistically stationary mean value of the turbulent flame speed has been reached. The results are stored in a table that could be used by large scale premixed combustion models, e.g. front tracking schemes. First results are compared quantitatively with direct numerical simulations (DNS) taken from literature. Then it is illustrated in one example how the new method could help to fix constants in algebraic models for turbulent flame speeds. Further it is shown how the technique can be extended to incorporate turbulent strain effects. Finally we investigate the effect of the use of detailed and tabulated chemistry under unsteady conditions.}, language = {en} } @misc{Weber2009, author = {Weber, Marcus}, title = {A Subspace Approach to Molecular Markov State Models via an Infinitesimal Generator}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11432}, number = {09-27}, year = {2009}, abstract = {Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.}, language = {en} }