### Refine

#### Year of publication

- 2003 (63) (remove)

#### Document Type

- Report (24)
- Preprint (19)
- Doctoral Thesis (16)
- Article (1)
- Diploma Thesis (1)
- Periodical Part (1)
- Working Paper (1)

#### Language

- English (63) (remove)

#### Is part of the Bibliography

- no (63)

#### Keywords

- AG-RESY (4)
- Wavelet (4)
- Mehrskalenanalyse (3)
- CAD (2)
- CHAMP (2)
- Gravitationsfeld (2)
- Inverses Problem (2)
- Lineare Algebra (2)
- Mathematikunterricht (2)
- Modellierung (2)
- Navier-Stokes-Gleichung (2)
- RODEO (2)
- RONAF (2)
- Up Functions (2)
- linear algebra (2)
- mathematical education (2)
- modelling (2)
- numerical simulation (2)
- praxisorientiert (2)
- wavelets (2)
- : Navier-Stokes equations (1)
- : Two-phase flow in porous media (1)
- : multiple criteria optimization (1)
- : multiple objective programming (1)
- Abel integral equations (1)
- Algebraische Geometrie (1)
- Approximation (1)
- Archimedische Kopula (1)
- Asiatische Option (1)
- Assembly (1)
- Basket Option (1)
- Bessel functions (1)
- Biot-Savart Operator (1)
- Biot-Savart operator (1)
- Bitvektor (1)
- Blocked Neural Networks (1)
- Brinkman (1)
- Brownian motion (1)
- Brownsche Bewegung (1)
- Cauchy-Navier-Equation (1)
- Cauchy-Navier-Gleichung (1)
- Chi-Quadrat-Test (1)
- Cholesky-Verfahren (1)
- Clusterion (1)
- Clusterverbindungen (1)
- Code Inspection (1)
- Continuum Damage (1)
- Decomposition and Reconstruction Schemes (1)
- Deformationstheorie (1)
- Discrete linear systems (1)
- Dislocations (1)
- Druckkorrektur (1)
- Dynamic cut (1)
- Earliest arrival augmenting path (1)
- Elastische Deformation (1)
- Elastoplasticity (1)
- Elliptische Verteilung (1)
- Entwurfsautomation (1)
- Erdmagnetismus (1)
- Erfüllbarke (1)
- Euler's equation of motion (1)
- Expected shortfall (1)
- Extreme value theory (1)
- Filtergesetz (1)
- Finite Elements (1)
- Finite-Elemente-Methode (1)
- Finite-Volumen-Methode (1)
- Flachwasser (1)
- Flachwassergleichungen (1)
- Folgar-Tucker equation (1)
- Force-Torque (1)
- Fourier-Transformation (1)
- Fräsen (1)
- Garbentheorie (1)
- Glättung (1)
- Glättungsparameterwahl (1)
- Gruppenoperation (1)
- Hals-Nasen-Ohren-Chirurgie (1)
- Hals-Nasen-Ohren-Heilkunde (1)
- Hankel matrix (1)
- Harmonische Spline-Funktion (1)
- Heavy-tailed Verteilung (1)
- Heston model (1)
- High-Spin-Komplexe (1)
- Hochschild homology (1)
- Hochschild-Homologie (1)
- Homologietheorie (1)
- Hub-and-Spoke-System (1)
- Hybridregler (1)
- Hydratation (1)
- Hydrostatischer Druck (1)
- Hörgerät (1)
- Immobilienaktie (1)
- Implantation (1)
- Infrared Multiphoton Dissociation Spectroscopy (IR-MPD) (1)
- Infrarotspek (1)
- Integer programming (1)
- Inverse problems in Banach spaces (1)
- Ionensolvatation (1)
- Knowledge Extraction (1)
- Kopula <Mathematik> (1)
- Kraftregelung (1)
- Kreditrisiko (1)
- L-curve Methode (1)
- Label correcting algorithm (1)
- Label setting algorithm (1)
- Lagrangian relaxation (1)
- Lavrentiev regularization for equations with monotone operators (1)
- Layout (1)
- Lineare Elastizitätstheorie (1)
- Lineare Optimierung (1)
- Locally Supported Radial Basis Functions (1)
- Logiksynthese (1)
- MO-Theorie (1)
- Manipulation skills (1)
- Marktrisiko (1)
- Martingaloptimalitätsprinzip (1)
- Mastoid (1)
- Mastoidektomie (1)
- Material-Force-Method (1)
- Mehrkriterielle Optimierung (1)
- Model checking (1)
- Modellbildung (1)
- Modulraum (1)
- Molekülorbital (1)
- Multicriteria decision making (1)
- Multiple criteria analysis (1)
- Multiresolution Analysis (1)
- Multisresolution Analysis (1)
- Multivariate Wahrscheinlichkeitsverteilung (1)
- Navier-Stokes (1)
- Network flows (1)
- Nonlinear Regression (1)
- Nonlinear multigrid (1)
- Nonparametric time series (1)
- Numerische Strömungssimulation (1)
- Oberflächenmaße (1)
- Ohrenchirurgie (1)
- Optimierung (1)
- Option pricing (1)
- Optionsbewertung (1)
- Optionspreistheorie (1)
- PI-Regler (1)
- Permutationsäquivalenz (1)
- Plastizitätstheorie (1)
- Polyhedron (1)
- Portfolio-Optimierung (1)
- Poröser Stoff (1)
- Protonentransfer (1)
- Quantile autoregression (1)
- Quasi-identities (1)
- RTL (1)
- Reflection (1)
- Regelung (1)
- Regler (1)
- Reglerentwurf (1)
- Regularisierung (1)
- Regularität (1)
- Riemannian manifolds (1)
- Riemannsche Mannigfaltigkeiten (1)
- Risikomanagement (1)
- Roboter (1)
- Robotics (1)
- Robotik (1)
- SIMPLE (1)
- SWARM (1)
- Satellitengeodäsie (1)
- Scale function (1)
- Schadensmechanik (1)
- Schaltwerk (1)
- Schädelchirurgie (1)
- Shallow Water Equations (1)
- Simplex (1)
- Singly Occupied Molecular Orbital (SOMO) (1)
- Spherical (1)
- Spherical Wavelets (1)
- Spline-Approximation (1)
- Stein equation (1)
- Stochastische Processe (1)
- Stratifaltigkeiten (1)
- Stücklisten (1)
- Symmetrie (1)
- Symmetriebrechung (1)
- System-on-Chip (1)
- Tail Dependence Koeffizient (1)
- Value at Risk (1)
- Vektorkugelfunktionen (1)
- Vektorwavelets (1)
- Verifikation (1)
- Vorverarbeitung (1)
- Wavelet-Theorie (1)
- Wavelet-Theory (1)
- Wirbelabtrennung (1)
- Wirbelströmung (1)
- Zugesicherte Eigenschaft (1)
- Zyklische Homologie (1)
- adaptive local refinement (1)
- adaptive refinement (1)
- adaptive triangulation (1)
- algebraic geometry (1)
- archimedean copula (1)
- asian option (1)
- associated Legendre functions (1)
- asymptotic homogenization (1)
- automated analog circuit design (1)
- basket option (1)
- batch presorting problem (1)
- behavioral modeling (1)
- bills of materials (1)
- bitvector (1)
- bounded model checking (1)
- circuit sizing (1)
- cliquet options (1)
- clustering and disaggregation techniques (1)
- competetive analysis (1)
- computer algebra (1)
- conditional quantiles (1)
- consecutive ones property (1)
- coupled flow in plain and porous media (1)
- cyclic homology (1)
- decision support systems (1)
- deformable objects (1)
- design automation (1)
- dif (1)
- discrete facility location (1)
- discrete location (1)
- efficient set (1)
- elasticity problem (1)
- elliptical distribution (1)
- evolutionary algorithms (1)
- expert system (1)
- fatigue (1)
- fiber orientation (1)
- flood risk (1)
- force control (1)
- force following (1)
- forward starting options (1)
- fuzzy logic (1)
- genetic algorithms (1)
- geomagnetism (1)
- global pressure (1)
- gravimetry (1)
- gravitational field recovery (1)
- group action (1)
- harmonic density (1)
- hybrid control (1)
- hyper-quasi-identities (1)
- hypergeometric functions (1)
- hyperquasivarieties (1)
- incident wave (1)
- incompressible flow (1)
- injection molding (1)
- integer programming (1)
- interactive navigation (1)
- kernel estimate (1)
- knowledge management (1)
- knowledge representation (1)
- kraftbasiertes Führen (1)
- layout (1)
- lid-driven flow in a (1)
- linear optimization (1)
- logic synthesis (1)
- logistics (1)
- macro modeling (1)
- martingale optimality principle (1)
- mastoid (1)
- mastoidectomy (1)
- model reduction (1)
- moduli space (1)
- multigrid methods (1)
- multileaf collimator (1)
- multiphase mixture model (1)
- multiscale modeling (1)
- multiscale structures (1)
- multivariate chi-square-test (1)
- non-Newtonian flow in porous media (1)
- non-commutative geometry (1)
- non-local conditions (1)
- nonlinear term structure dependence (1)
- oil filters (1)
- online optimization (1)
- option pricing (1)
- otorhinolaryngological surgery (1)
- parameter choice (1)
- polynomial algorithms (1)
- portfolio-optimization (1)
- praxis orientated (1)
- preprocessing (1)
- pressure correction (1)
- project management and scheduling (1)
- projection-type splitting (1)
- property cheking (1)
- quantile autoregression (1)
- quasi-P (1)
- quasi-SH (1)
- quasi-SV (1)
- quasivarieties (1)
- radiation therapy (1)
- real-life applications. (1)
- refraction (1)
- regularity (1)
- representative systems of Pareto solutions (1)
- satisfiability (1)
- scaling functions (1)
- sequential circuit (1)
- set covering (1)
- sheaf theory (1)
- simplex (1)
- singular spaces (1)
- singularity (1)
- singuläre Räume (1)
- software development (1)
- spherical splines (1)
- stability (1)
- stochastic processes (1)
- stochastic volatility (1)
- stop location (1)
- strategic (1)
- strength (1)
- subgradient (1)
- supply chain management (1)
- surface measures (1)
- symbolic analysis (1)
- symmetry (1)
- system simulation (1)
- tail dependence coefficient (1)
- technology mapping (1)
- time series (1)
- toric geometry (1)
- torische Geometrie (1)
- triclinic medium (1)
- uniform consistency (1)
- value-at-risk (1)
- variable neighborhood search (1)
- various formulations (1)
- vector spherical harmonics (1)
- vectorial wavelets (1)
- verification (1)
- vertical velocity (1)
- vertikale Geschwindigkeiten (1)
- visual (1)
- visual interfaces (1)
- vortex seperation (1)
- Überflutung (1)
- Überflutungsrisiko (1)

#### Faculty / Organisational entity

In many robotic applications, the teaching of points in space is necessary to register the robot coordinate system with the one of the application. Robot-human interaction is awkward and dangerous for the human because of the possibly large size and power of the robot, so robot movements must be predictable and natural. We present a novel hybrid control algorithm which provides the needed precision in small scale movements while allowing for fast and intuitive large scale translations.

The original publication is available at www.springerlink.com. This original publication also contains further results. We study a spherical wave propagating in radius- and latitude-direction and oscillating in latitude-direction in case of fibre-reinforced linearly elastic material. A function system solving Euler's equation of motion in this case and depending on certain Bessel and associated Legendre functions is derived.

In this article, we consider the problem of planning inspections and other tasks within a software development (SD) project with respect to the objectives quality (no. of defects), project duration, and costs. Based on a discrete-event simulation model of SD processes comprising the phases coding, inspection, test, and rework, we present a simplified formulation of the problem as a multiobjective optimization problem. For solving the problem (i.e. finding an approximation of the efficient set) we develop a multiobjective evolutionary algorithm. Details of the algorithm are discussed as well as results of its application to sample problems.

The Earth's surface is an almost perfect sphere. Deviations from its spherical shape are less than 0,4% of its radius and essentially arise from its rotation. All equipotential surfaces are nearly spherical, too. In consequence, multiscale modelling of geoscientifically relevant data on the sphere involving rotational symmetry of the trial functions used for the approximation plays an important role. In this paper we deal with isotropic kernel functions showing local support and (one-dimensional) polynomial structure (briefly called isotropic finite elements) for reconstructing square--integrable functions on the sphere. Essential tool is the concept of multiresolution analysis by virtue of the spherical up function. The main result is a tree algorithm in terms of (low--order) isotropic finite elements.

We generalize the classical shortest path problem in two ways. We consider two - in general contradicting - objective functions and introduce a time dependency of the cost which is caused by a traversal time on each arc. The resulting problem, called time-dependent bicriteria shortest path problem (TdBiSP) has several interesting practical applications, but has not attained much attention in the literature.

This report explains basic notions and concepts of Abstract State Machines (ASM) as well as notation for defining ASM models. The objective here is to provide an intuitive understanding of the formalism; for a rigorous definition of the mathematical foundations of ASM, the reader is referred to [2] and [3]. Further references on ASM-related material can be found on the ASM Web Pages [1].

Annual Report 2002
(2003)

Asymptotic homogenisation technique and two-scale convergence is used for analysis of macro-strength and fatigue durability of composites with a periodic structure under cyclic loading. The linear damage accumulation rule is employed in the phenomenological micro-durability conditions (for each component of the composite) under varying cyclic loading. Both local and non-local strength and durability conditions are analysed. The strong convergence of the strength and fatigue damage measure as the structure period tends to zero is proved and their limiting values are estimated.

This publication tries to develop mathematical subjects for school from realistic problems. The center of this report are business planning and decision problems which occur in almost all companies. The main topics are: Calculation of raw material demand for given orders, consumption of existing stock and the lot sizing.

One of the main goals of an organization developing software is to increase the quality of the software while at the same time to decrease the costs and the duration of the development process. To achieve this, various decisions e.ecting this goal before and during the development process have to be made by the managers. One appropriate tool for decision support are simulation models of the software life cycle, which also help to understand the dynamics of the software development process. Building up a simulation model requires a mathematical description of the interactions between di.erent objects involved in the development process. Based on experimental data, techniques from the .eld of knowledge discovery can be used to quantify these interactions and to generate new process knowledge based on the analysis of the determined relationships. In this paper blocked neuronal networks and related relevance measures will be presented as an appropriate tool for quanti.cation and validation of qualitatively known dependencies in the software development process.

The focus of this work has been to develop two families of wavelet solvers for the inner displacement boundary-value problem of elastostatics. Our methods are particularly suitable for the deformation analysis corresponding to geoscientifically relevant (regular) boundaries like sphere, ellipsoid or the actual Earth's surface. The first method, a spatial approach to wavelets on a regular (boundary) surface, is established for the classical (inner) displacement problem. Starting from the limit and jump relations of elastostatics we formulate scaling functions and wavelets within the framework of the Cauchy-Navier equation. Based on numerical integration rules a tree algorithm is constructed for fast wavelet computation. This method can be viewed as a first attempt to "short-wavelength modelling", i.e. high resolution of the fine structure of displacement fields. The second technique aims at a suitable wavelet approximation associated to Green's integral representation for the displacement boundary-value problem of elastostatics. The starting points are tensor product kernels defined on Cauchy-Navier vector fields. We come to scaling functions and a spectral approach to wavelets for the boundary-value problems of elastostatics associated to spherical boundaries. Again a tree algorithm which uses a numerical integration rule on bandlimited functions is established to reduce the computational effort. For numerical realization for both methods, multiscale deformation analysis is investigated for the geoscientifically relevant case of a spherical boundary using test examples. Finally, the applicability of our wavelet concepts is shown by considering the deformation analysis of a particular region of the Earth, viz. Nevada, using surface displacements provided by satellite observations. This represents the first step towards practical applications.

Clusters bridge the gap between single atoms or molecules and the condensed phase and it is the challenge of cluster science to obtain a deeper understanding of the molecular foundation of the observed cluster specific properties/reactivities and their dependence on size. The electronic structure of hydrated magnesium monocations [Mg,nH2O]+, n<20, exhibits a strong cluster size dependency. With increasing number of H2O ligands the SOMO evolves from a quasi-valence state (n=3-5), in which the singly occupied molecular orbital (SOMO) is not yet detached from the metal atom and has distinct sp-hybrid character, to a contact ion pair state. For larger clusters (n=17,19) these ion pair states are best described as solvent separated ion pair states, which are formed by a hydrated dication and a hydrated electron. With growing cluster size the SOMO moves away from the magnesium ion to the cluster surface, where it is localized through mutual attractive interactions between the electron density and dangling H-atoms of H2O ligands forming "molecular tweezers" HO-H (e-) H-OH. In case of the hydrated aluminum monocations [Al,nH2O]+,n=20, different isomers of the formal stoichiometry [Al,20H2O]+ were investigated by using gradient-corrected DFT (BLYP) and three different basic structures for [Al,20H2O]+ were identified: (a) [AlI(H2O)20]+ with a threefold coordinated AlI; (b) [HAlIII(OH)(H2O)19]+ with a fourfold coordinated AlIII; (c) [HAlIII(OH)(H2O)19]+ with a fivefold coordinated AlIII. In ground state [AlI(H2O)20]+ (a) which contains aluminum in oxidation state +1 the 3s2 valence electrons remain located at the aluminium monocation. Different than for open shell magnesium monocations no electron transfer into the hydration shell is observed for closed shell AlI. However, clusters of type (a) are high energy isomers (DE»+190 kJ mol-1) and the activation barrier for reaction into cluster type (b) or (c) is only approximately 14 kJ mol-1. The performed ab initio calculations reveal that unlike in [Mg,nH2O]+, n=7-17, for which H atom eliminiation is found to be the result of an intracluster redoxreaction, in [Al,nH2O]+,n=20, H2 is formed in an intracluster acid-base reaction. In [Mg,nH2O]+, n>17, the magnesium dication was found to coexist with a hydrated electron in larger cluster sizes. This proves that intermolecular electron delocalization - previously almost exclusively studied in (H2O)n- and (NH3)n- clusters - can also be an important issue for water clusters doped with an open shell metal cation or a metal anion. Structures and stabilities of hydrated magnesium water cluster anions with the formal stoichiometry [Mg,nH2O]-, n=1-11, were investigated by application of various correlated ab initio methods (MP2, CCSD, CCSD(T)). Metal cations surely have high relevance in numerous biological processes, and as most biological processes take place in aqueous solution hydrated metal ions will be involved. However, in biological systems solvent molecules (i.e. water) compete with different solvated chelate ligands for coordination sites at the metal ion and the solvent and chelate ligands are in mutual interactions with each other and the metal ion. These interactions were investigated for the hydration of ZnII/carnosine complexes by application of FT-ICR-MS, gas-phase H/D exchange experiments and supporting ab initio calculations. In the last chapter of this work the Free Electron Laser IR Multi Photon Dissocition (FEL-IR-MPD) spectra of mass selected cationic niobium acetonitrile complexes with the formal stoichiometry [Nb,nCH3CN]+, n=4-5, in the spectral range 780 – 2500 cm-1 are reported. In case of n=4 the recorded vibrational bands are close to those of the free CH3CN molecule and the experimental spectra do not contain any evident indication of a potential reaction beyond complex formation. By comparison with B3LYP calculated IR absorption spectra the recorded spectra are assigned to high spin (quintet, S=2), planar [NbI(NCCH3)4]+. In [Nb,nCH3CN]+, n=5, new vibrational bands shifted away from those of the acetonitrile monomer are observed between 1300 – 1550 cm-1. These bands are evidence of a chemical modification due to an intramolecular reaction. Screening on the basis of B3LYP calculated IR absorption spectra allow for an assignment of the recorded spectra to the metallacyclic species [NbIII(NCCH3)3(N=C(CH3)C(CH3)=N)]+ (triplet, S=1), which has formed in a internal reductive nitrile coupling reaction from [NbI(NCCH3)5]+. Calculated reaction coordinates explain the experimentally observed differences in reactivity between ground state [NbI(NCCH3)4]+ and [NbI(NCCH3)5]+. The reductive nitrile coupling reaction is exothermic and accessible (Ea=49 kJ mol-1) only in [NbI(NCCH3)5]+, whereas in [NbI(NCCH3)4]+ the reaction is found to be endothermic and retarded by significantly higher activation barriers (Ea>116 kJ mol-1).

Objective: In some surgical specialties, e.g. orthopedics, robots are already used in the operating room for bony milling work. Oto- and otoneurosurgery may also greatly benefit by robotic enhanced precision. Study Design: Experimental study on robotic milling on oak wood and human temporal bone specimen. Methods: A standard industrial robot with a 6 degrees-of-freedom serial kinematics was used with force feedback to proportionally control the robot speed. Different milling modes and characteristic path parameters were evaluated to generate milling paths based on CAD geometry data of a cochlear implant and an implantable hearing system. Results: The best suited strategy proofed to be the spiral horizontal milling mode with the burr held perpendicularly to the temporal bone surface. In order to avoid high grooves, the distance in between paths should equal half the radius of the cutting burr head. Due to the vibration of the robot’s own motors, a rather high oscillation of the standard deviation of forces was encountered. This oscillation dropped drastically to nearly 0 N, when the burr head reached contact with the dura mater due to its damping characteristics. The cutting burr could be moved a long time on the dura without damaging it, because of its rather blunt head. The robot moved the burr very smoothly according to the encountered resistances. Conclusion: This is the first development of an functioning robotic milling procedure for otoneurosurgery with force-based speed control. It is planned to implement ultrasound-based local navigation and to perform robotic mastoidectomy.

The objective of the present article is to give an overview of an application of Fuzzy Logic in Regulation Thermography, a method of medical diagnosis support. An introduction to this method of the complementary medical science based on temperature measurements – so-called thermograms – is provided. The process of modelling the physician’s thermogram evaluation rules using the calculus of Fuzzy Logic is explained.

The thesis discusses discrete-time dynamic flows over a finite time horizon T. These flows take time, called travel time, to pass an arc of the network. Travel times, as well as other network attributes, such as, costs, arc and node capacities, and supply at the source node, can be constant or time-dependent. Here we review results on discrete-time dynamic flow problems (DTDNFP) with constant attributes and develop new algorithms to solve several DTDNFPs with time-dependent attributes. Several dynamic network flow problems are discussed: maximum dynamic flow, earliest arrival flow, and quickest flow problems. We generalize the hybrid capacity scaling and shortest augmenting path algorithmic of the static network flow problem to consider the time dependency of the network attributes. The result is used to solve the maximum dynamic flow problem with time-dependent travel times and capacities. We also develop a new algorithm to solve earliest arrival flow problems with the same assumptions on the network attributes. The possibility to wait (or park) at a node before departing on outgoing arc is also taken into account. We prove that the complexity of new algorithm is reduced when infinite waiting is considered. We also report the computational analysis of this algorithm. The results are then used to solve quickest flow problems. Additionally, we discuss time-dependent bicriteria shortest path problems. Here we generalize the classical shortest path problems in two ways. We consider two - in general contradicting - objective functions and introduce a time dependency of the cost which is caused by a travel time on each arc. These problems have several interesting practical applications, but have not attained much attention in the literature. Here we develop two new algorithms in which one of them requires weaker assumptions as in previous research on the subject. Numerical tests show the superiority of the new algorithms. We then apply dynamic network flow models and their associated solution algorithms to determine lower bounds of the evacuation time, evacuation routes, and maximum capacities of inhabited areas with respect to safety requirements. As a macroscopic approach, our dynamic network flow models are mainly used to produce good lower bounds for the evacuation time and do not consider any individual behavior during the emergency situation. These bounds can be used to analyze existing buildings or help in the design phase of planning a building.

In this paper we discuss an earliest arrival flow problem of a network having arc travel times and capacities that vary with time over a finite time horizon T. We also consider the possibility to wait (or park) at a node before departingon outgoing arc. This waiting is bounded by the value of maximum waiting time and the node capacity which also vary with time.

The Discrete Ordered Median Problem (DOMP) generalizes classical discrete location problems, such as the N-median, N-center and Uncapacitated Facility Location problems. It was introduced by Nickel [16], who formulated it as both a nonlinear and a linear integer program. We propose an alternative integer linear programming formulation for the DOMP, discuss relationships between both integer linear programming formulations, and show how properties of optimal solutions can be used to strengthen these formulations. Moreover, we present a specific branch and bound procedure to solve the DOMP more efficiently. We test the integer linear programming formulations and this branch and bound method computationally on randomly generated test problems.

Extensions of Shallow Water Equations The subject of the thesis of Michael Hilden is the simulation of floods in urban areas. In case of strong rain events, water can flow out of the overloaded sewer system onto the street and damage the connected houses. The dependable simulation of water flow out of a manhole ("manhole") and over a curb ("curb") is crucial for the assessment of the flood risks. The incompressible 3D-Navier-Stokes Equations (3D-NSE) describe the free surface flow of water accurately, but require expensive computations. Therefore, the less CPU-intensive (factor ca.1/100) Shallow Water Equations (SWE) are usually applied in hydrology. They can be derived from 3D-NSE under the assumption of a hydrostatic pressure distribution via depth-integration and are applied successfully in particular to simulations of river flow processes. The SWE-computations of the flow problems "manhole" and "curb" differ to the 3D-NSE results. Thus, SWE need to be extended appropriately to give reliable forecasts for flood risks in urban areas within reduced computational efforts. These extensions are developed based on physical considerations not considered in the classical SWE. In one extension, a vortex layer on the ground is separated from the main flow representing its new bottom. In a further extension, the hydrostatic pressure distribution is corrected by additional terms due to approximations of vertical velocities and their interaction with the flow. These extensions increase the quality of the SWE results for these flow problems up to the quality level of the NSE results within a moderate increase of the CPU efforts.