Anmerkung: Intro -- Preface -- Contents -- Part I Methods -- Calculation of Chemical Equilibria in Multi-Phase: Multicomponent Systems -- 1 Introduction -- 2 Problem Formulation -- 2.1 Non-Ideal Gibbs Function -- 2.2 Stoichiometric Constraints -- 2.3 The Optimization Problem -- 3 Methodology for the Calculation of Chemical Equilibria -- 3.1 Reformulation of the Minimization Problem -- 3.2 Discretization of the H-Problem -- 3.3 Corrector Step -- 4 Automated Detection of Miscibility Gaps -- 5 Results -- 5.1 Gibbs Free Energy Minimization Using BePhaSys -- 5.2 Calculation of Two-Dimensional Phase Diagrams: Interpolation and Parallelization -- Appendix: The Gibbs Free Energy Function -- References -- LC-GAP: Localized Coulomb Descriptors for the Gaussian Approximation Potential -- 1 Introduction -- 2 Potential Energy Prediction Through Machine Learning -- 2.1 The GAP Framework and Gaussian Process Regression -- 2.2 Localized Coulomb Matrix Descriptors -- 3 Results -- 3.1 Comparison of Descriptor Functions on QM7 -- 3.2 Larger Datasets and Prediction of Multiple Properties -- 3.3 Distribution of Individual Atomic Contributions -- 4 Conclusions and Future Work -- References -- River Bed Morphodynamics: Metamodeling, Reliability Analysis, and Visualization in a Virtual Environment -- 1 Introduction -- 2 RBF Metamodel -- 3 Quantile Estimation -- 3.1 Sensitivity-Based Approach -- 3.1.1 First-Order Approximation -- 3.1.2 Second-Order Approximation -- 3.2 Monte Carlo -- 3.3 Weighted Monte Carlo -- 3.4 Quasi-Monte Carlo (QMC) -- 3.5 Quasi-Random Splines (QRS) -- 4 Numerical Tests -- 5 Visualization in Virtual Environment -- 6 Conclusion -- References -- Cooling Circuit Simulation I: Modeling -- 1 Introduction -- 2 Network -- 3 Water Pipes -- 3.1 Continuum Mechanics -- 3.2 Simplifying Assumptions -- 3.3 Discretization and Regularization -- 4 Further Devices. , 4.1 Resistors and Valves -- 4.2 Pumps -- 4.3 Heat Exchangers -- 5 Element Control -- 6 Conclusion -- References -- Part II Products -- Algebraic Multigrid: From Academia to Industry -- 1 Introduction -- 2 From Geometric to Algebraic Multigrid -- 3 The Early Phase of Algebraic Multigrid (1982-1987) -- 3.1 The First Documented AMG Application -- 3.2 The Basics of `Classical' AMG -- 4 The Renaissance of AMG (1995-2000) -- 4.1 Resumption of Major Research on AMG -- 4.2 Towards Industry -- 4.2.1 Computational Fluid Dynamics -- 4.2.2 Streamline Approach in Oil Reservoir Simulation -- 5 The Main AMG Development Phase (2000-Today) -- 5.1 The General Trend -- 5.2 Bridging the Gap -- 5.3 SAMG for Coupled PDE Systems -- 5.3.1 Unknown-Based Approach -- 5.3.2 Point-Based Approach -- 5.3.3 Status of the Solver Framework SAMG -- 6 Industry-Driven Applications -- 6.1 Semiconductor Applications -- 6.2 Multi-Ion Transport and Reaction -- 6.3 Oil Reservoir Simulation -- 6.3.1 The Reservoir Simulation Models -- 6.3.2 Fully Implicit Methods -- 7 Summary, Conclusions and Lessons Learned -- References -- Parallel Algebraic Multigrid -- 1 Introduction -- 2 Challenges Imposed by Parallel Computer Architectures -- 2.1 Single Core Performance: CPU Clock Speed and Memory Frequency -- 2.2 Multi-Core CPUs and Shared Memory Parallelism -- 2.2.1 Multi-Core and Memory Access -- 2.2.2 Intrinsically Serial Components -- 2.2.3 Race Conditions -- 2.2.4 Multiple Sockets -- 2.3 Distributed Memory Parallelism -- 3 How SAMG Counters the HPC Challenges -- 3.1 Tuning and Parallelization of Smoothing -- 3.2 Ruge-Stüben Coarsening -- 3.3 Coarse Grid Solution -- 4 SCAI's Parallel SAMG Solver Library -- References -- MpCCI: Neutral Interfaces for Multiphysics Simulations -- 1 Introduction -- 2 MpCCI CouplingEnvironment -- 2.1 Aero-Elasticity and Fluid-Structure-Interaction. , 2.1.1 Wing and Spoiler Design -- 2.1.2 Hydraulic Pump Layout -- 2.2 Thermal and Vibration Loads in Turbomachinery -- 2.2.1 Thermal Loads on Ceramic Impeller -- 2.2.2 Life-Time Estimation of Turbine Blades -- 2.3 Vehicle Dynamics and Nonlinear Component Behavior -- 2.3.1 Driving Over Obstacles -- 2.3.2 Wading Simulation for Off-Road Vehicles -- 2.4 Automotive Thermal Management -- 2.4.1 Automotive Thermal Management for Full Vehicles -- 2.4.2 Automotive Thermal Management for Vehicle Manifolds -- 2.5 Component Design in Electrical Engineering -- 2.5.1 Cooling of a 3-Phase Transformer -- 2.5.2 Electric Arc in Switching Devices -- 3 MpCCI FSIMapper -- 4 MpCCI Mapper Solution for Integrated Simulation Workflows -- 4.1 Passive Safety -- 4.2 Forming Tools and Material Properties -- 4.2.1 Lightweight Stamping Tools: Use Forming Loads in Structural Optimization -- 4.2.2 Validation of Material Model Parameters: Compare Forming Results and Experimental Data -- 4.3 Composite Structures and Plastic Components -- 4.3.1 CFRP Workflows: From Draping via Mulling and Curing to Structural Analysis -- 4.3.2 Structural Integrity of Blow Moulded Plastic Components -- 5 Conclusion -- References -- Cooling Circuit Simulation II: A Numerical Example -- 1 Introduction -- 2 Application -- 2.1 Cooling System -- 2.2 Circuit Basics and Example -- 3 Concept and Software -- 3.1 Framework and Components -- 3.2 Semi-Automatic Model Creation with Schemparser -- 3.3 Device Modeling and Sensor Mapping -- 3.4 Collection of Measurement Data with PowerDAM -- 3.5 Nonlinear Problem Setup and Solution with MYNTS -- 4 Numerical Tests -- 4.1 Simplified Heat Exchanger -- 4.2 Logarithmic Mean Temperature Difference -- 5 Conclusion -- References -- The LAMA Approach for Writing Portable Applications on Heterogenous Architectures -- 1 Introduction -- 2 LAMA -- 2.1 Heterogeneous Memory. , 2.2 Heterogeneous Kernel -- 2.3 Task Parallelism -- 2.4 Distributed Memory Support -- 2.5 Matrices and Vectors -- 2.6 Solver Framework -- 2.7 Extensibility and Maintainability -- 3 Performance Comparison -- 4 Summary -- Appendix -- Test Environment -- Test Matrices -- References -- ModelCompare -- 1 Introduction -- 2 Development History -- 3 Capabilities -- 3.1 Detection of Geometry Changes -- 3.2 Detection of MultiParts -- 3.3 Spotwelds and Rigid Body Elements -- 3.4 Detection of Material-ID and Thickness Changes -- 4 Outlook -- References -- Rapid Enriched Simulation Application Development with PUMA -- 1 Introduction -- 2 Partition of Unity Methods -- 3 PUMA Framework Design -- 4 Application Examples -- 5 Concluding Remarks -- References -- Part III Applications and Show Cases -- Applying CFD for the Design of an Air-Liquid Interface In-Vitro Testing Method for Inhalable Compounds -- 1 Introduction -- 2 In-Vitro Air-Liquid Interface -- 3 Simulating the Aerosol Conduction System -- 4 Simulating the Liquid Supply System -- 4.1 Clogging in Liquid Channels -- 5 Simulating an Aerosol Sampling Box -- 6 Conclusions -- References -- A Mapping Procedure for the Computation of Flow-Induced Vibrations in Turbomachinery -- 1 Introduction -- 2 Nonlinear Harmonic Method -- 3 Mapping of Pressure Excitations -- 3.1 Periodic Models and Nodal Diameters -- 3.2 Deriving Excitation and Responding Shape -- 3.3 Summary -- 4 Application Example -- 4.1 Harmonic CFD Simulation -- 4.2 Mapping -- 4.3 Harmonic Structural Analysis -- 5 Conclusion -- References -- Molecular Dynamics Simulation of Membrane Free Energy Profiles Using Accurate Force Field for Ionic Liquids -- 1 Introduction -- 2 Computational Methods -- 2.1 Simulation Details -- 2.1.1 Technical Details -- 2.1.2 Force Field Development for [C2MIM][EtSO4] -- 2.2 Umbrella Sampling -- 3 Results and Discussion. , 3.1 Force Field Development for [C2MIM][EtSO4] -- 3.1.1 Density -- 3.1.2 Self-Diffusion Coefficients -- 3.1.3 Heat of Vaporization -- 3.1.4 Shear Viscosity -- 3.2 Free Energy Profiles -- 4 Outlook and Conclusion -- 4.1 Outlook: Towards Fully Automated Force Field Development -- 4.1.1 Case Study: Automated Parameterization of Ethylene Oxide -- 4.2 Conclusion -- References -- The cloud4health Project: Secondary Use of Clinical Data with Secure Cloud-Based Text Mining Services -- 1 Introduction -- 2 Developing a Secure Cloud-Solution for Medicine -- 2.1 Existing Cloud Solutions for Medicine -- 2.2 Requirements for Cloud Infrastructures Arising from Patient Data Processing -- 2.3 Security Mechanisms -- 2.4 Secure Cloud Infrastructure -- 2.4.1 Secure Clinical Gateway to the Cloud -- 2.4.2 Data Processing Flow -- 2.4.3 End-to-End Encryption -- 2.4.4 Multi-Tenancy and No Data Persistence -- 3 Clinical Text Mining Solutions -- 3.1 Short Literature Overview -- 3.2 General Architecture of the Text Mining Services -- 3.3 Overview Use Cases -- 3.3.1 General Use Case Process Model -- 3.4 Mining Endoprosthetic Surgery Reports -- 3.5 Mining Pathology Reports -- 4 Discussion -- References -- Dimensionality Reduction for the Analysis of Time Series Data from Wind Turbines -- 1 Introduction -- 2 Time Series Characteristics in Wind Energy -- 2.1 Numerical Simulations of Wind Turbines -- 2.2 Condition Monitoring of Wind Turbines -- 3 Exploration of Time Series Data from Numerical Simulations -- 3.1 Virtual Sensor Data from Wind Turbine Simulations -- 3.2 Nonlinear Dimensionality Reduction for Time Series Analysis -- 3.3 Diffusion Maps -- 3.4 Numerical Results -- 4 Anomaly Detection Based on Linear Dimensionality Reduction for Condition Monitoring Sensor Data from Wind Turbines -- 4.1 Sensor Data from Rotor Blades -- 4.1.1 Pre-processing. , 4.2 Anomaly Detection in Sensor Data.

Anmerkung: Intro -- Preface -- Contents -- Part I Scaling Limits of Diffusion Processes and Singular Spaces -- Ricci Bounds for Euclidean and Spherical Cones -- 1 Introduction -- 1.1 Statement of the Main Results -- 1.2 Basic Definitions and Notations -- 1.3 The Curvature-Dimension Condition -- 2 Euclidean Cones over Metric Measure Spaces -- 3 Spherical Cones over Metric Measure Spaces -- References -- A Monotone Approximation to the Wasserstein Diffusion -- 1 Introduction and Statement of the Main Results -- 2 Dirichlet-Ferguson Process, Entropic Measure and Wasserstein Diffusion -- 2.1 The Dirichlet-Ferguson Process -- 2.2 The Dirichlet Form on G -- 2.3 The Dirichlet Form on the Wasserstein Space -- 3 The Distribution of Random Means -- 4 The Measure mkβ in the Multivariate Case -- 5 Projections, Isomorphisms, Approximations -- 5.1 Finite Dimensional Projections -- 5.2 Monotone Convergence -- 5.3 Isomorphisms I -- 5.4 Standard Approximations -- 5.5 Isomorphisms II -- 5.6 Isomorphisms III -- 6 Convergence -- 6.1 Convergence of Finite Dimensional Distributions -- 6.2 Convergence of Processes -- 6.3 Final Remarks -- References -- Adapted Function Spaces for Dispersive Equations -- 1 Introduction -- 2 The Bounded p Variation -- 2.1 Step Functions and Ruled Functions -- 2.2 The Spaces Vp and Up -- 2.3 Embeddings -- 3 Dispersive Equations -- 3.1 Adapted Function Spaces -- 3.2 The Generalized KdV Equation -- 3.3 The Kadomtsev-Petviashvili II Equation -- 3.4 The Energy Critical Nonlinear Schrrödinger Equation on Compact Manifolds -- References -- A Note on Metastable Behaviour in the Zero-Range Process -- 1 Introduction -- 1.1 The Model and Basic Properties -- 2 Metastability -- 2.1 Definitions and Results -- 3 Results for the Zero-Range Process -- 4 Proofs of the Results -- 4.1 Capacity -- 4.1.1 Lower Bound -- 4.1.2 Upper Bound -- 4.2 Proofs of Theorems 3 and 4. , 4.3 Metastability of the Zero-Range Process -- References -- Convergence of the Two-Point Function of the Stationary TASEP -- 1 Introduction and Result -- 2 Setting and Strategy of the Proof -- 3 Proof of Proposition 1: Upper Tail -- 3.1 Asymptotics for -- 3.2 Evaluation of g1 -- 3.3 Estimations on g2 and g3 -- 4 Proof of Proposition 2: Lower Tail -- 5 Proof of Corollary 2 -- References -- Part II Multiple Scales in Mathematical Models of Materials Science and Biology -- Vortex Motion for the Landau-Lifshitz-Gilbert Equation with Applied Magnetic Field -- 1 Introduction -- 2 Jacobian, Vorticity and Renormalized Energy -- 2.1 Compactness -- 2.2 The Renormalized Energy -- 2.3 The Thiele Equation -- 3 LLG Equation with External Fields -- 3.1 Conservation Laws -- 3.2 Weak Solutions and Bubbling -- 4 Convergence and Vortex Trajectories -- 5 Motion Law -- References -- On Prandtl-Reuss Mixtures -- 1 Introduction -- 2 Mathematical Formulation of the Problem -- 2.1 Basic Setting -- 2.2 Balance of Linear Momentum -- 2.3 Elasticity -- 2.4 The Variational Inequality for Elastic-Perfect-Plastic Mixtures -- 3 The Penalty Equation -- 3.1 Reconstruction of Partial Strains -- 4 The Rothe Approximation -- 4.1 Definition and Solvability of the Rothe Approximation -- 4.2 First Estimates for the Rothe Approximation -- 5 Estimates for the Rothe Approximation -- 6 Convergence of the Rothe Method -- 7 L∞(L2)-Estimate for the Time Derivatives of the Stresses -- 8 Passage to the Limit as the Penalty Parameter μ Tends to Zero -- 9 A Model for the Volume Fraction α and the Yield Parameter Depending on the History of the Rate of the Plastic Strain of the Soft Material -- References -- Modeling and Simulation of Lipid Monolayers as Surfactant in Lung Alveoli -- 1 Biological Function of Surfactant Lipids for the Breathing Cycle -- 2 Microscale Stochastic Multi-particle Model. , 3 Mesoscale Continuum Mixture Model -- 4 Sharp Phase Transition Approximation -- 4.1 Case of Dissolving Ordered Monolayer: λ> -- 0 -- 4.2 Case of Growing Ordered Monolayer: λ< -- 0 -- 4.3 Simulation Results -- 5 One-Dimensional Simulation of the Continuum Phase Field Model -- 5.1 Smoothed Phase Separation in a Fixed Interval -- 5.2 Phase Separation Behavior in an Oscillating Domain Simulating ``Breathing'' -- 6 Conclusions -- References -- Fluid Mixtures and Applications to Biological Systems -- 1 Introduction -- 2 Fluid Mixtures -- 3 Exploiting the Free Energy Inequality -- 4 Remark on Pressure -- 5 Examples -- 6 Handling Gradient Terms -- 7 Polymerization of Actin Filaments -- 8 The Quasistatic Problem -- 9 Fractional Densities -- 10 Diffusion Limit -- 11 Polymer Mixtures Including Gradients -- 12 Conclusion -- References -- A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow -- 1 Introduction -- 2 Review of the Time Discretization of Isotropic Willmore Flow -- 3 Nested Time Discretization for Anisotropic Willmore Flow -- 4 Finite Element Discretization in Space -- 5 Optimization Algorithm for the Time Steps -- 6 Numerical Results -- References -- Energy Scaling and Domain Branching in Solid-Solid PhaseTransitions -- 1 Introduction -- 2 Upper Bounds -- 2.1 The Case of Two Rank-One Connections -- 2.2 The Case of One Rank-One Connection -- 3 Lower Bound -- 3.1 The Case of Two Rank-One Connections -- 3.2 The Case of One Rank-One Connection -- 4 Outlook -- References -- Part III Numerics for Multiscale Models and Singular Phenomena -- On a Multilevel Preconditioner and its Condition Numbersfor the Discretized Laplacian on Full and Sparse Grids in HigherDimensions -- 1 Introduction -- 2 Discretization -- 2.1 Discretization by an Isotropic Full-Grid -- 2.2 The Multilevel Approach. , 2.3 A Norm Equivalence Based on Orthogonal Subspaces -- 3 A Dimension-Independent Full Grid Preconditioner -- 3.1 Orthogonalization Operator -- 3.2 Preconditioner -- 3.3 Cost Discussion for the New Preconditioner -- 4 Sparse Grids -- 4.1 Definition -- 4.2 Sparse Grid Submatrix and Preconditioner -- 4.3 Cost Discussion -- 5 Prewavelets -- 5.1 Preconditioner -- 5.2 Cost Discussion -- 6 Numerical Experiments -- 7 Concluding Remarks -- References -- Simulation of Droplet Impact with Dynamic Contact Angle Boundary Conditions -- 1 Introduction -- 2 The Moving Contact Line Problem -- 2.1 Modeling Issues -- 2.2 Numerical Issues -- 3 Mathematical Model -- 3.1 The Navier-Stokes Solver -- 3.2 The Contact Angle as a Boundary Condition -- 3.3 The Dynamic Contact Angle Model by Yokoi et al. (C1) -- 3.4 The Dynamic Contact Angle Model by Shikhmurzaev (C2) -- 4 The Numerical Method -- 4.1 Discretization of the Navier-Stokes Equations and the Level-Set Method -- 4.2 Discretization of the Contact Angle Boundary Condition -- 4.3 Implementation of the Contact Angle Models -- 4.4 Methods for Mass Conservation -- 5 Numerical Results -- 5.1 The Contact Angle Model by Yokoi -- 5.2 The Contact Angle Model by Shikhmurzaev -- 5.3 Mass Conservation -- 6 Conclusion -- References -- A Parallel Multiscale Simulation Toolbox for Coupling Molecular Dynamics and Finite Elements -- 1 Introduction -- 1.1 Related Work -- 1.2 Article Contribution and Outline -- 2 Multiscale Simulation Method -- 2.1 Molecular Dynamics -- 2.2 Continuum Mechanics and Finite Elements -- 2.3 Coupling Method -- 2.3.1 Coupling with Overlap -- 2.3.2 Damping High Fluctuation Modes -- 2.3.3 Complete Algorithm -- 3 Multiscale Simulation Toolbox -- 3.1 Interface Design -- 3.1.1 Opaque Handles -- 3.1.2 Access Epochs -- 3.1.3 Piggybacking of Metadata -- 3.2 Description of the Maci Code -- 4 Parallelization Aspects. , 4.1 Challenges -- 4.2 Data Distribution in the Maci Code -- 4.3 Parallel Assembly -- 4.4 Runtime Support -- References -- A Moving Least Squares Approach to the Construction of Discontinuous Enrichment Functions -- 1 Introduction -- 2 Particle Data -- 3 The Moving Least Squares Method -- 4 Adjacency Based Modification -- 5 Proof of Concept -- 6 Concluding Remarks -- References -- Second Moment Analysis for Robin Boundary Value Problems on Random Domains -- 1 Introduction -- 2 Robin Boundary Value Problems on Random Domains -- 3 Variational Formulation -- 4 Solving Tensor Product Boundary Value Problems -- 4.1 An Abstract View on the Linearization Approach -- 4.2 Sparse Tensor Product Spaces -- 4.3 Sparse Multilevel Frames -- 4.4 Combination Technique -- 4.5 Low-Rank Approximation -- 5 Finite Element Discretization -- 5.1 Parametric Finite Elements -- 5.2 Galerkin Discretization -- 5.3 Implementation of the Combination Technique -- 5.4 Implementation of the Low-Rank Approximation -- 6 Numerical Results -- 6.1 Model Verification -- 6.2 A Correlation Kernel of Arbitrary Smoothness -- 6.3 A Correlation Kernel of Finite Smoothness -- 7 Concluding Remarks -- References -- Simulation of Q-Tensor Fields with Constant Orientational Order Parameter in the Theory of Uniaxial Nematic Liquid Crystals -- 1 Introduction and Derivation of the Mathematical Setting -- 2 Euler Lagrange Equations for ELdG and EOF -- 3 Discrete Setting -- 3.1 Monotonicity Estimates -- 3.2 Euler Lagrange Equation in the Discrete Setting -- 4 Iterative Algorithms -- 4.1 Fully Discrete Algorithm for Discrete Harmonic Director Fields -- 4.2 Fully Discrete Algorithm for Discrete Q Harmonic Tensor Fields -- 5 Analysis of the Algorithms and Q Harmonic Tensor Fields -- 5.1 Stability and Convergence of the Tensor Field Algorithm -- 5.2 Weak Compactness Result for Q Harmonic Tensor Fields. , 6 Numerical Experiments.

Anmerkung: Intro -- Copyright -- Table of Contents -- Preface -- Introduction -- Index.