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ویرایش: نویسندگان: Fred J. Vermolen, Cornelis Vuik سری: Lecture Notes in Computational Science and Engineering, 139 ISBN (شابک) : 3030558738, 9783030558734 ناشر: Springer سال نشر: 2021 تعداد صفحات: 1269 [1185] زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 58 Mb
در صورت تبدیل فایل کتاب Numerical Mathematics and Advanced Applications ENUMATH 2019: European Conference, Egmond aan Zee, The Netherlands, September 30 - October 4 به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب ریاضیات عددی و کاربردهای پیشرفته ENUMATH 2019: کنفرانس اروپایی، Egmond aan Zee، هلند، 30 سپتامبر - 4 اکتبر نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
این کتاب مقالات برجسته ارائه شده در کنفرانس اروپایی ریاضیات عددی و کاربردهای پیشرفته (ENUMATH 2019) را گردآوری می کند. این کنفرانس توسط دانشگاه صنعتی دلفت سازماندهی شد و از 30 سپتامبر تا 4 اکتبر 2019 در شهر اگموند آن زی هلند برگزار شد و کارشناسان برجسته این حوزه آخرین نتایج و ایده ها را در خصوص طراحی، پیاده سازی و تحلیل الگوریتم های عددی ارائه کردند. و همچنین کاربرد آنها برای مشکلات اجتماعی مرتبط.
ENUMATH مجموعهای از کنفرانسهایی است که هر دو سال یک بار برای بحث در مورد جنبههای اساسی و گرایشهای جدید در ریاضیات عددی و کاربردهای علمی و صنعتی برگزار میشود که همه بررسی شدهاند. در بالاترین سطح تخصص بین المللی اولین ENUMATH در سال 1995 در پاریس برگزار شد، با اقساط متوالی در سایت های مختلف در سراسر اروپا، از جمله هایدلبرگ (1997)، جیواسکیلا (1999)، lschia Porto (2001)، پراگ (2003)، سانتیاگو د کمپوستلا (2005)، گراتس ( 2007)، اوپسالا (2009)، لستر (2011)، لوزان (2013)، آنکارا (2015) و برگن (2017).
This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, implementation and analysis of numerical algorithms, as well as their applications to relevant societal problems.
ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).
Preface Contents High Order Whitney Forms on Simplices and the Questionof Potentials 1 Introduction 2 The Continuous Side of the de Rham's Diagram 3 The Discrete Side of the de Rham's Diagram 4 Notions from Graph Theory 5 From Fields to Potentials References The Candy Wrapper Problem: A Temporal Multiscale Approach for PDE/PDE Systems 1 Introduction: The Candy Wrapper Problem 2 Model Configuration 2.1 Governing Equations 2.2 Parameters 2.3 ALE Formulation and Discretization 3 Temporal Multiscales 4 Numerical Results 4.1 Convergence of the Averaging Scheme for Periodic Flow Problems 4.2 Simulation of the Candy Wrapper Problem 5 Outlook and Discussion References Systematisation of Systems Solving Physics Boundary ValueProblems 1 Introduction 2 Differential Geometric Models 2.1 Formal Sums of Field Configurations 2.2 Differentiation and the Action Principle 3 Concretization of Particular Models 4 Some Numerical Experiments with Space-Time Models 4.1 Transforming Cavity 4.2 Local Time-Stepping and Stability 5 Conclusions References On the Convergence of Flow and Mechanics Iterative Coupling Schemes in Fractured Heterogeneous Poro-Elastic Media 1 Introduction 2 Model 3 Fixed Stress Split in Fractured Poro-Elastic Media 4 Convergence in Heterogeneous Media 4.1 Assumptions 4.2 Discretization 5 Banach Contraction Result 5.1 Proof References Finite Difference Solutions of 2D Magnetohydrodynamic Channel Flow in a Rectangular Duct 1 Introduction 2 Mathematical Formulation 3 Implementation of FDM and Boundary Conditions 4 Numerical Results and Discussion 5 Conclusion References Applications of the PRESB Preconditioning Method for OPT-PDE Problems 1 Introduction 2 The PRESB Preconditioning Method 3 A Basic Optimal Control Problem 4 An Inverse Identification Problem for a Non-selfadjoint Problem 4.1 Problem Formulation 4.2 The Reduced Matrix System and Its Nonsingularity References Model Order Reduction Framework for Problems with Moving Discontinuities 1 Introduction 2 Mathematical Formulation 3 Numerical Experiments 3.1 Single Wavefront Scenario 3.2 Multiple Wavefront Scenario 3.3 Discussion 4 Conclusions References Numerical Simulation of a Phase-Field Model for Reactive Transport in Porous Media 1 Introduction 2 The Two-Scale Phase-Field Model 3 The Multi-Scale Iterative Scheme 4 A Numerical Example References A Structure-Preserving Approximation of the Discrete Split Rotating Shallow Water Equations 1 Introduction 2 Split Hamiltonian FE Discretization of the RSW Slice-Model 2.1 Continuous and Discrete Split Hamiltonian RSW Slice-Model 2.2 Family of Structure-Preserving Split RSW Schemes 2.3 A Structure-Preserving Approximation of Split RSW Schemes 3 Numerical Results 4 Conclusions References Iterative Coupling for Fully Dynamic Poroelasticity 1 Introduction 2 Variational Formulation of a Semi-Discrete Approximation of the System of Dynamic Poroelasticity 3 Iterative Coupling for the System of Dynamic Poroelasticity 4 Convergence of the Iterative Coupling Scheme References A Time-Dependent Parametrized Background Data-WeakApproach 1 Introduction 2 Basic Notation and Best-Knowledge (bk) Models 3 Time-Dependent PBDW 3.1 Limited-Observations Statement 3.2 Offline Stage 4 Numerical Results References Comparison of the Influence of Coniferous and Deciduous Trees on Dust Concentration Emitted from Low-Lying Highway by CFD 1 Introduction 2 Physical and Mathematical Model 2.1 Fluid Flow 2.2 Turbulence 2.3 Particles Transport 2.4 Vegetation Model 2.5 Numerical Method 3 The Numerical Experiment Setting 4 Results: Efficiency of the Barriers 5 Conclusions References A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models 1 Introduction 2 Mathematical Model and Temporal Discretization 3 Linearization and Domain Decomposition 3.1 Existence of Solutions and Convergence 4 Numerical Experiment 5 Conclusion References An Adaptive Penalty Method for Inequality Constrained Minimization Problems 1 Introduction 2 Problem Formulation and Solution Methods 2.1 Primal-Dual Active Set Method 2.2 Penalty Method 3 The Adaptive Penalty Method 4 Numerical Results References Multipreconditioning with Application to Two-Phase Incompressible Navier–Stokes Flow 1 Introduction 2 Multipreconditioned GMRES (MPGMRES) 3 Selective MPGMRES (sMPGMRES) 4 Numerical Results for sMPGMRES References On the Dirichlet-to-Neumann Coarse Space for Solving the Helmholtz Problem Using Domain Decomposition 1 Introduction 2 Discretisation and Solver Methodology 3 The Dirichlet-to-Neumann Coarse Space 4 Numerical Results 5 Conclusions References A Comparison of Boundary Element and Spectral Collocation Approaches to the Thermally Coupled MHD Problem 1 Introduction 2 Physical Problem and Mathematical Formulation 3 Numerical Methods 3.1 Application of CSCM 3.2 Application of DRBEM 4 Results and Discussions 5 Conclusion References Minimal Sets of Unisolvent Weights for High Order Whitney Forms on Simplices 1 High Order Whitney Forms 2 Small Simplices 3 A Minimal Set of Unisolvent Weights References Experimental Comparison of Symplectic and Non-symplectic Model Order Reduction on an Uncertainty Quantification Problem 1 Introduction 2 Symplectic Model Order Reduction for Parametrized Hamiltonian Systems 3 Model Order Reduction and Uncertainty Quantification 4 Numerical Experiment 5 Summary and Outlook References 3D-2D Stokes-Darcy Coupling for the Modelling of Seepage with an Application to Fluid-Structure Interaction with Contact 1 Introduction 2 The Coupled Stokes-Darcy System 3 The Fluid-Structure-Poroelastic-Contact Interaction System 4 Numerical Experiments 4.1 Stokes-Darcy Example 4.2 Fluid-Structure Interaction with Contact References A Second Order Time Integration Method for the Approximation of a Parabolic 2D Monge-Ampère Equation 1 Introduction 2 Model Problem 3 Numerical Algorithm 4 Finite Element Discretization 5 Numerical Experiments 5.1 A Polynomial Example 5.2 An Exponential Example References Local Flux Reconstruction for a Frictionless Unilateral Contact Problem 1 Introduction 2 Model Problem and Discrete Formulation 3 Definition of Locally Reconstructed Flux 3.1 Equivalent Mixed Formulation 3.2 Local Computation of the Multiplier 3.3 Conservative Locally Reconstructed Flux 4 A Posteriori Error Analysis 4.1 A Posteriori Error Estimator 4.2 Upper Error Bound References Study on an Adaptive Finite Element Solver for the Cahn–Hilliard Equation 1 Phase Separation in Electrode Particles 2 The Numerical Method 3 Numerical Experiments 4 Conclusion References Numerical Study of the Fracture Diffusion-Dispersion Coefficient for Passive Transport in Fractured Porous Media 1 Introduction 2 The Differential Model 2.1 Notation 2.2 Advective Velocity Fields 2.3 Diffusion-Dispersion Tensors 2.4 The Reduced Model 3 Numerical Experiments 3.1 Injection and Production Wells 3.2 Impermeable Fractures 3.3 Permeable Fractures References Several Agent-Based and Cellular Automata Mathematical Frameworks for Modeling Pancreatic Cancer 1 Introduction 2 Agent-Based Models 3 The Cellular Automata Model 4 Uncertainty Quantification 5 Discussion and Conclusions References Error Bounds for Some Approximate Posterior Measures in Bayesian Inference 1 Introduction 2 Error Bounds for Approximate Posteriors 2.1 Error Bounds for Random Approximate Posteriors 2.2 Error Bounds for Random Forward Models 3 Conclusions and Directions for Future Work References High-Order Two and Three Level Schemes for Solving Fractional Powers of Elliptic Operators 1 Introduction 2 Symmetrical Euler Method 3 Non-uniform and Adaptive Time Meshes 3.1 Adaptive Mesh 4 Three Level Scheme 5 High-Order Schemes 6 Conclusions References Numerical Investigation of the Boussinesq Equations Through a Subgrid Artificial Viscosity Method 1 Introduction 2 Subgrid Artificial Viscosity Scheme 3 Numerical Analysis 4 Numerical Experiments 4.1 Numerical Convergence Study 4.2 Marsigli's Flow Experiment 4.3 Thermal Distribution in Buoyancy Driven Cavity 5 Conclusion References FFT-Based Solution Schemes for the Unit Cell Problem in Periodic Homogenization of Magneto-Elastic Coupling 1 Introduction 2 Mathematical Formulation 3 Periodic Homogenization 3.1 Cell Problem 3.2 Homogenized Problem 4 Spectral Schemes on the Unit Cell 4.1 Periodic Lippmann–Schwinger Equations 4.2 Algorithms 5 Numerics 6 Conclusion References Novel Flux Approximation Schemes for Systems of Coupled Advection-Diffusion-Reaction Equations 1 Introduction 2 Mathematical Model of Multi-Component Diffusion 3 Special Case: Homogeneous Flux Scheme for a Coupled Diffusion-Reaction System 4 Numerical Example References PDE-Constrained Optimization: Optimal Control with L1-Regularization, State and Control Box Constraints 1 Introduction 2 Problem Formulation and Optimality System 3 Preconditioning 4 Solvers, Tolerances and Termination Criteria 5 Numerical Illustrations 6 Concluding Remarks References A Time-Simultaneous Multigrid Method for Parabolic Evolution Equations 1 Motivation 2 Time-Simultaneous Multigrid 2.1 Intuitive Explanation for Small and Large Time Steps 2.2 Characteristics of the Proposed Method 3 Numerical Results 4 Conclusion References Computing Function of Large Matrices by a Preconditioned Rational Krylov Method 1 Rationale 2 Rational Krylov Approximation for f(An)v 3 A Sequence of Preconditioners for the Rational Krylov Subspace 4 What Subspace Are We Computing in Practice? 5 Numerical Test 6 Conclusions References On Energy Preserving High-Order Discretizations for Nonlinear Acoustics 1 Introduction 2 A Canonical Form of the Westervelt Equation 3 Structure-Preserving Discretization 4 Remarks on the Implementation 5 Numerical Tests References Hierarchical DWR Error Estimates for the Navier-Stokes Equations: h and p Enrichment 1 Introduction 2 The Model Problem and Discretization 2.1 The Model Problem 2.2 Discretization 3 Dual Weighted Residual Method and Error Representation 3.1 The Adjoint Problem 3.2 Error Estimation and Adaptive Algorithm 4 Numerical Experiment 4.1 Quantities of Interest 4.2 Discussion of the Results References Towards Confident Bayesian Parameter Estimation in Stochastic Chemical Kinetics 1 Introduction 2 Bayesian Inversion of the Circadian Rhythm 2.1 The Circadian Rhythm by Vilar et al. 2.2 Prior Information Content 2.3 Summarizing Statistics 2.4 Posterior Distribution and Prediction 3 Discussion References Strategies for the Vectorized Block Conjugate Gradients Method 1 Introduction 2 Block Krylov Subspaces 3 Block Conjugate Gradient Method 4 Implementation and Numerical Experiments 5 Conclusion and Outlook References The Unfitted HHO Method for the Stokes Problem on CurvedDomains 1 Introduction 2 The Unfitted HHO Method 2.1 The Local Discrete Problem 2.2 The Global Discrete Problem 2.3 Stability and Error Estimates 3 Numerical Simulations References A Non-reflective Boundary Condition for LBM Based on the Assumption of Non-equilibrium Symmetry 1 Introduction 2 The Boltzmann Transport Equation 3 The Lattice Boltzmann Method 4 The Multiple-Relaxation-Time Collision Model 5 The Non-equilibrium Symmetry Boundary 6 Test Case 1: Propagation of Acoustic Waves 7 Test Case 2: Convected Vortex 8 Summary Reference ALE Space-Time Discontinuous Galerkin Method for the Interaction of Compressible Flow with Linear and Nonlinear Dynamic Elasticity and Applications to Vocal Fold Vibrations 1 Compressible Navier-Stokes Problem in a Time Dependent Domain and Dynamic Elasticity Problem 1.1 Compressible Flow 1.2 Dynamic Elasticity 1.3 Transmission Conditions 2 Discretization 2.1 Discretization of the Flow Problem 2.2 Discretization of the Elasticity Problem 3 Numerical Experiments References Efficient Solvers for a Stabilized Three-Field Mixed Formulation of Poroelasticity 1 Introduction 2 Local Pressure Jump Stabilization 2.1 Linear Solver 3 Numerical Results 3.1 Barry-Mercer's Problem 3.2 Cantilever Problem 4 Conclusion References Time-Dependent Two-Dimensional Fourth-Order Problems: Optimal Convergence 1 Introduction 2 The Equation ∂t u+2 u =f 3 Numerical Results References Accurate Numerical Eigenstates of the Gross-Pitaevskii Equation 1 Introduction 2 The Mathematical Model 2.1 Discretisation 3 The Picard Iteration Scheme 4 Results for the Picard Method 5 The Constrained Newton Method 6 Results for the Constrained Newton Method 7 Conclusion References Basic Machine Learning Approaches for the Acceleration of PDE Simulations and Realization in the FEAT3 Software 1 Introduction 2 FEAT3: Unconventional High Performance Finite Elements 2.1 Trends in Modern Hardware and Green HPC 2.2 Finite Elements and the Need for Speed 2.3 Fast Linear Solvers Based on Geometric Multigrid Methods 2.4 FEAT3: FEM+GMG Meets UCHPC 3 A Concise Machine Learning Framework to Accelerate Linear Solvers 3.1 Poisson Problem and Anisotropies 3.2 Approximate Inverses with Neural Network 3.3 Neural Networks for Anisotropic Meshes 4 Conclusion and Future Work References Deflated Preconditioned Conjugate Gradients for Nonlinear Diffusion Image Enhancement 1 Introduction 2 PCG Methods with Subdomain Deflation 2.1 DPCG 2.2 Three Different Choices for the Deflation Vectors Thresholding Region Growing Same Size Patches 2.3 Preconditioner 3 Experimental Results 3.1 Simulated Shepp-Logan Image 3.2 Measured Shepp-Logan Image 4 Conclusions References Coupled Flow and Mechanics in a 3D Porous Media with LineSources 1 Introduction 2 Mathematical Model and Discretization 2.1 Singularity Removal Method 2.2 Fixed-Stress Splitting Scheme 3 Numerical Results References A Semismooth Newton Solution of the Steady-State Non-isothermal Bingham Flow with Temperature Dependent Nonlocal Parameters 1 Problem Statement 2 Regularization and Numerical Approach 2.1 Discretization and Semismooth Newton Algorithm 3 Numerical Results References A Sequential Sensor Selection Strategy for Hyper-Parameterized Linear Bayesian Inverse Problems 1 Introduction 2 A Hyper-Parameterized Bayesian Inverse Problem 3 Numerical Stability and A-Optimal Experimental Design 4 Sensor Selection Strategy 5 Numerical Results 6 Conclusion References Biomechanical Surrogate Modelling Using Stabilized Vectorial Greedy Kernel Methods 1 Introduction 2 Stabilized VKOGA Algorithm 3 Application to Spine Modelling 4 Numerical Experiments 5 Conclusion and Outlook References Augmented Lagrangian Method for Thin Plates with Signorini Boundaries 1 Introduction 2 The Kirchhoff Plate Model 3 Finite Element Method 4 Numerical Results 4.1 Point Load in the Center of the Plate 4.2 Point Load at (3/4,3/4) References A Hybrid High-Order Method for Flow Simulations in Discrete Fracture Networks 1 The Flow Problem in Fractured Rocks 2 The HHO Method for Solving Flow in DFN 3 Computation of the Equivalent Permeability with the HHO Method 4 Performance Obtained with the NEF++ Software 5 Conclusion References Fully Algebraic Two-Level Overlapping Schwarz Preconditioners for Elasticity Problems 1 Introduction 2 Model Problems 2.1 GDSW and RGDSW Preconditioners 3 Fully Algebraic Construction of GDSW and RGDSW Coarse Spaces 4 Numerical Results References Stationary Flow Predictions Using Convolutional Neural Networks 1 Introduction 2 CFD Simulations 3 Surrogate Convolutional Neural Network 4 Results 5 Conclusion References Discontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation 1 Introduction 2 Geometric Parametrization 3 Discontinuous Galerkin Formulation 4 Affine Expansion 5 Reduced Basis Method 6 A Numerical Example 7 Some Concluding Remarks References An Efficient Numerical Scheme for Fully Coupled Flow and Reactive Transport in Variably Saturated Porous Media Including Dynamic Capillary Effects 1 Introduction 2 The Numerical Schemes 2.1 The Monolithic Newton Method (MON-NEWTON) 2.2 The Monolithic L-Scheme (MON-LS) 2.3 The Splitting Approach (NonLinS) 2.4 The Mixed Linearization Scheme 3 Numerical Examples 4 Conclusions References Multistage Preconditioning for Adaptive Discretization of Porous Media Two-Phase Flow 1 Introduction 2 Structure of the Jacobian Matrix 3 Constrained Pressure Residual Preconditioner 3.1 Method Description CPR Procedure 3.2 Decoupling Operators 4 CPR Preconditioner Performances 5 Conclusion References Biorthogonal Boundary Multiwavelets 1 Introduction 2 Biorthogonal Multiwavelets 3 Refinable Boundary Functions 4 Refinable Linear Combinations 5 The Biorthogonal Setting 6 Algorithm 7 Example 8 Summary References Machine Learning in Adaptive FETI-DP: Reducing the Effort in Sampling 1 Introduction 2 Linear Elasticity and an Adaptive FETI-DP Algorithm 3 Machine Learning for Adaptive FETI-DP 4 Numerical Results References A New Algebraically Stabilized Method for Convection–Diffusion–Reaction Equations 1 Introduction 2 Finite Element Discretization 3 Algebraic Flux Correction 4 A New Algebraically Stabilized Method 5 Numerical Results References Analysis of Kuramoto-Sivashinsky Model of Flame/Smoldering Front by Means of Curvature Driven Flow 1 Introduction 2 Computational Studies of the KS Model 3 Rotating Wave Solution 4 Conclusions References The Master-Slave Splitting Extended to Power Flow Problems on Integrated Networks with an Unbalanced Distribution Network 1 Introduction 2 Characterization of the Power Flow Problem 2.1 Integrated Networks 3 Solving the Power Flow Problem with the Master-Slave Splitting Method 3.1 The Master-Slave Splitting Extended to Balanced/Unbalanced Networks The Master-Slave Iterative Schemes 4 Numerical Assessment of Integration Methods 5 Conclusion References On Mesh Regularity Conditions for Simplicial Finite Elements 1 Introduction 2 Main Definitions and Concepts 2.1 Volumic Regularity Conditions 2.2 Minimum Angle Conditions in Higher Dimensions 3 The Maximum Angle Conditions 4 Final Remarks and Some Open Problems References Assembly of Multiscale Linear PDE Operators 1 Introduction 2 Multiscale Assembler 3 Trace Constrained Systems 4 More General Multiscale Systems References A Least-Squares Galerkin Gradient Recovery Method for Fully Nonlinear Elliptic Equations 1 Introduction 2 A Least-Squares Galerkin Approach to Gradient Recovery for Linear Equations in Nondivergence Form 3 Linearization of Fully Nonlinear Problems 4 Numerical Experiments References A Posteriori Model Error Analysis of 3D-1D Coupled PDEs 1 Introduction 2 Problem Setting 2.1 Reduced 3D-1D Coupled Problem 3 A-posteriori Model Error Analysis 3.1 Localization of the Model Error Approximated Representation Formula Local Error Estimator 4 Results References CG Variants for General-Form Regularization with an Application to Low-Field MRI 1 Introduction 2 GCGLS and GCGME 2.1 Comparison of the Condition Numbers: A Simple Case 2.2 GCGLS and GCGME for IRLS 3 Experiments 4 Numerical Results 5 Conclusion References Data-Driven Modeling for Wave-Propagation 1 Introduction 2 Theory 2.1 Example: Constant Coefficients 3 Algorithm 4 Numerical Results 4.1 Harmonic Oscillator 4.2 1D Wave-Equation 5 Conclusion and Discussion References Numerical Simulation of Coupled Electromagnetic and Thermal Problems in Permanent Magnet Synchronous Machines 1 Introduction 2 Thermal Analysis of Electrical Machines 3 Verification of the Proposed Coupled Model 3.1 Case 1: The First Example: BMW C1 11kW Electric Motor 3.2 Case 2: The Second Example: Toyota Prius 2004 Electric Motor 4 Conclusions References Parameter Robust Preconditioning for Multi-Compartmental Darcy Equations 1 Introduction 2 Lack of Parameter Robustness in Standard Formulation 3 Change of Variables Yields Parameter Robust Formulation 4 Numerical Examples for the New Formulation 5 Conclusion References Scaling of the Steady-State Load Flow Equations for Multi-Carrier Energy Systems 1 Introduction 2 Steady-State Load Flow 3 Scaling 3.1 Per Unit System 3.2 Matrix Scaling 4 Newton-Raphson 5 Numerical Results 6 Conclusion References A Semismooth Newton Method for Regularized Lq-quasinorm Sparse Optimal Control Problems 1 Introduction 2 The Optimal Control and Its Optimality Conditions 2.1 The Optimality System 3 The DC: Semismooth Newton Method 4 Numerical Examples References Monotone and Second Order Consistent Scheme for the Two Dimensional Pucci Equation 1 Introduction 2 Discretization 2.1 Selling's Formula 2.2 The Pucci Operator 3 Numerical Experiments 4 Conclusion References A Multi-Scale Flow Model for Studying Blood Circulation in Vascular System 1 Introduction 2 Materials and Methods 2.1 Flow Model 2.2 Tracer Concentration Flow 2.3 Model Implementation 3 Result and Discussion 4 Conclusion References The 8T-LE Partition Applied to the Barycentric Divisionof a 3-D Cube 1 Introduction 2 The Barycentric Partition of a 3D-Cube 3 The 8T-LE Partition 3.1 The 8T-LE Partition of the Sommerville Tetrahedron Number 3 (ST3) 3.2 The 8T-LE Partition of the Regular Right-Type Tetrahedron 3.3 The 8T-LE Partition of the Isosceles Trirectangular Tetrahedron The Quasi Right-Type Tetrhedron and the New Tetrahedron 3.4 Classes of Similarity Generated 4 Main Results References Point Forces and Their Alternatives in Cell-Based Models for Skin Contraction 1 Introduction 2 Mathematical Models 2.1 Elasticity Equation and Point Sources in One Dimension 2.2 Elasticity Equation and Point Sources in Two Dimensions 3 Numerical Results 4 Conclusion References Empirically Driven Orthonormal Bases for Functional DataAnalysis 1 Introduction 2 FD and Their Representations 3 Data Driven Choice of the Knots 4 Application: Efficient Analysis of the Quarter Vehicle Model 5 Simulation Studies 6 Conclusions References Uniqueness for a Second Order Gradient Flow of Elastic Networks 1 Introduction 2 Proof of Uniqueness Reference A Second Order Finite Element Method with Mass Lumping for Wave Equations in H(div) 1 Motivation 2 Problem Statement and Finite Element Approximation 3 Auxiliary Results 4 Convergence Analysis 5 Implementation and Mass Lumping 6 Numerical Illustration Reference Model Order Reduction of Combustion Processes with Complex Front Dynamics 1 Introduction 2 Basic Idea: 1D Example—Advective Transport 3 2D Example: Moving Disc 4 Front Transport Reconstruction (FTR) 5 2D Example: Application to Combustion 6 Discussion and Conclusion References Modelling of the Influence of Vegetative Barrier on Particulate Matter Concentration Using OpenFOAM 1 Introduction 2 Mathematical Model 3 Numerical Solvers 3.1 Wall Functions 4 Results 4.1 Full-Scale Unperturbed ABL 4.2 Flow in and Around the Forest Canopy 5 Conclusions References Logistic Regression for Prospectivity Modeling 1 Introduction 2 Logistic Regression 3 General Logistic Regression with Endogenous Sampling 4 Algorithm 5 Computational Results 6 Conclusions References A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens 1 Introduction 2 Mathematical Formulation 3 Generalized Least-Squares Algorithm 4 Numerical Results References Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences 1 Introduction 2 Proper Orthogonal Decomposition for OFCP(μ)s 3 Results 3.1 Linear Time Dependent OFCP(μ) Governed by Stokes Equations 3.2 Non-linear Steady OFCP(μ) Governed by Navier-Stokes Equations 4 Concluding Remarks References Mathematical Assessment of the Role of Three Factors Entangled in the Development of Glaucoma by Means of the Ocular Mathematical Virtual Simulator 1 Introduction 2 The Ocular Mathematical Virtual Simulator 3 Numerical Study 3.1 Data 3.2 Simulation Results 3.3 Discussion 4 Conclusions References Well-Balanced and Asymptotic Preserving IMEX-Peer Methods 1 Introduction 2 Well-Balanced IMEX-Peer Methods 3 Asymptotic Preserving IMEX-Peer Methods 4 Numerical Examples References Approximation Schemes for Viscosity Solutions of Fully Nonlinear Stochastic Partial Differential Equations 1 Introduction 2 A Summary of the Main Results 2.1 The Scheme Operator 2.2 The Main Examples 3 The Convergence Proof: Monotonicity and Consistency 4 On the Construction of the Scheme Operator References Approximation Method with Stochastic Local Iterated Function Systems 1 Introduction 2 Local Iterated Function Systems and Local Fractal Functions 2.1 Hermite Type Local Fractal Functions References Optimal Control on a Model for Cervical Cancer 1 Introduction 2 Mathematical Model 3 The Optimum Control Problem 4 Numerical Simulation 5 Conclusion References Nitsche's Master-Slave Method for Elastic Contact Problems 1 Introduction 2 The Elastic Contact Problem 3 The Finite Element Methods 4 Error Estimates 5 Numerical Experiments References The Fixed-Stress Splitting Scheme for Biot's Equations as a Modified Richardson Iteration: Implications for OptimalConvergence 1 Introduction 2 The Quasi-Static Linear Biot Equations 3 The Discretized Biot Equations in Matrix Form 4 The Fixed-Stress Splitting Scheme as a Modified Richardson Iteration 4.1 Computing the Optimal Stabilization Parameter 5 Numerical Examples 6 Conclusions References Modeling and Simulation of Bed Dynamics in Oxyfuel Fluidized Bed Boilers 1 Introduction 2 MP-PIC Multiphase Flow Model 3 Solver Details 4 Solver Properties and Computational Results 5 Flow in Complex Geometry of the Experimental BFB Boiler 6 Conclusion and Further Work References Monotonicity Considerations for Stabilized DG Cut Cell Schemes for the Unsteady Advection Equation 1 A Stabilized DG Cut Cell Scheme for the Unsteady Advection Equation 2 Problem Setup for Piecewise Constant Polynomials 3 Monotonicity Considerations for Two Different Stabilization Terms 3.1 Unstabilized Case 3.2 Ghost Penalty Stabilization 3.3 Domain-of-Dependence Stabilization 4 Choice of η in DoD Stabilization 5 Numerical Results References Global Random Walk Solutions for Flow and Transport in Porous Media 1 Introduction 2 One-Dimensional GRW Algorithms 3 Two-Dimensional GRW Solutions of the Flow Problem 4 Statistical Inferences 5 Validation of the Flow and Transport GRW Solutions References On Finite Element Approximation of Aeroelastic Problems with Consideration of Laminar-Turbulence Transition 1 Introduction 2 Mathematical Description 3 Numerical Approximation 4 Numerical Results 5 Conclusion References Second-Order Time Accuracy for Coupled Lumped and Distributed Fluid Flow Problems via Operator Splitting: A NumericalInvestigation 1 Introduction 2 The Coupled PDE/ODE Problem Arising in Fluid Flow Modeling 3 A Second Order Operator Splitting Algorithm 4 Numerical Results 5 Conclusions and Outlook References A CSCM Approximation of Steady MHD Flow and Heat Transfer Between Parallel Plates with Hydrodynamic Slip and Convective Boundary Conditions 1 Introduction 2 Basic Equations for the Unsteady MHD Flow and Heat Transfer Between Parallel Plates 3 Application of the CSCM to MHD and Heat Transfer Equations 4 Numerical Results 5 Conclusion References Towards Scalable Automatic Exploration of Bifurcation Diagrams for Large-Scale Applications 1 Introduction 2 Overview of Available Software 3 Example: A Turing Problem 3.1 Partial Bifurcation Diagram of the BVAM Model 4 Comparison with LOCA 5 Conclusion References Generalized Monge–Ampère Equations for Freeform Optical System Design 1 Introduction 2 Mathematical Formulation 3 Least-Squares Algorithm 4 Numerical Example References A Direct Projection to Low-Order Level for p-Multigrid Methods in Isogeometric Analysis 1 Introduction 2 Model Problem and IgA Discretization 3 p-Multigrid Method 4 Numerical Results 5 Conclusions References The Concept of Prehandling as Direct Preconditioning for Poisson-Like Problems 1 Motivation 2 The Concept of Prehandling 3 The Hierarchical Finite Element Method 3.1 Idea and Realisation 3.2 Properties 3.3 Additional Prehandling via Partial Cholesky Decomposition 4 Numerical Results 5 Summary and Conclusion References Modal Analysis of Elastic Vibrations of Incompressible Materials Based on a Variational Multiscale Finite Element Method 1 Introduction 2 The Problem Definition 3 Stabilized Finite Element Approximation of the Eigenproblem 4 Modal Analysis of the Approximate Problem 5 A Numerical Test 6 Conclusion References A Learning-Based Formulation of Parametric Curve Fitting for Bioimage Analysis 1 Introduction 2 Description of the Method 2.1 Parametric Curve Model 2.2 Neural Network Architecture 2.3 Loss Function 3 Experimental Results 4 Discussion References Adaptive Time Stepping Methods Within a Data Assimilation Framework Applied to Non-isothermal Flow Dynamics 1 Introduction 2 Unsteady Gas Flow Equations 2.1 Numerical Discretization Runge–Kutta Schemes Rosenbrock Methods 3 Numerical Experiments 4 Conclusion References Matrix Oriented Reduction of Space-Time Petrov-Galerkin Variational Problems 1 Introduction 2 Space-Time Variational Formulation of PDEs 3 Petrov-Galerkin Discretizations 4 Efficient Numerical Methods for Tensorproduct Systems 5 Numerical Experiments References A Variational Formulation for LTI-Systems and Model Reduction 1 Introduction 2 Variational Formulation for LTI-Systems 3 Petrov-Galerkin (Detailed) Discretizations 4 Reduced Basis Method (RBM) 5 Numerical Experiments 6 Summary and Outlook References Numerical Solution of Traffic Flow Models 1 Macroscopic Traffic Flow Models 2 Discontinuous Galerkin Method 3 Implementation 4 Numerical Results 5 Conclusion References Numerical Approximation of Fluid-Structure Interaction Problem in a Closing Channel Near the Stability Boundary 1 Introduction 2 Mathematical Model 2.1 Elastic Body 2.2 Fluid Flow 2.3 Coupling Conditions 3 Numerical Method 3.1 Elastic Structure 3.2 Fluid Flow Finite Element Approximation 4 Numerical Results 5 Conclusion References Approximation Properties of Discrete Boundary Value Problems for Elliptic Pseudo-Differential Equations 1 Introduction 2 Digital Operators and Discrete Boundary Value Problems 3 Solvability and Comparison 3.1 Solvability 3.2 A Comparison References Mathematical and Numerical Models of Atherosclerotic Plaque Progression in Carotid Arteries 1 Introduction 2 Mathematical Models 3 Numerical Methods 4 Numerical Results References Equilibrium Path Analysis Including Bifurcations with an Arc-Length Method Avoiding A Priori Perturbations 1 Introduction 2 The Arc-Length Method 2.1 Conventional and Extended Arc-Length Method 2.2 Solution Methods for Complex Roots 2.3 Methods for Bifurcation Point Indication and Branch Switching 3 Benchmark Problem 4 Conclusions References Some Mathematical Properties of Morphoelasticity 1 Introduction 2 The Model for Morphoelasticity 3 Symmetry and Stability 3.1 Symmetry of the Strain Tensor 3.2 Linear Stability of 1D Morphoelasticity 4 Computer Simulations 4.1 The Numerical Method and Typical Results 4.2 Quantification of Uncertainty 5 Conclusions References Approximating Eigenvectors with Fixed-Point Arithmetic: A Step Towards Secure Spectral Clustering 1 Introduction 1.1 Related Work 1.2 Preliminaries Spectral Clustering The Lanczos Algorithm in R Computing in the Integer Domain 2 Lanczos Algorithm on Integers 3 Accuracy Analysis 3.1 Wisconsin Breast Cancer Dataset 4 Conclusions References Modelling Turbulent Combustion Coupled with Conjugate Heat Transfer in OpenFOAM 1 Introduction 2 Governing Equations and Numerical Models 2.1 Turbulence 2.2 Combustion 2.3 Energy 2.4 Thermal Radiation 3 Numerical Set-Up 3.1 Test Cases 4 Results and Discussion 4.1 Case 1 4.2 Case 2 5 Conclusions References Higher Order Regularity Shifts for the p-Poisson Problem 1 Introduction 2 Main Results 3 Further Results on Oscillations and Open Questions 4 Regularity of Vector Field Deformations References A Low-Rank Approach for Nonlinear Parameter-Dependent Fluid-Structure Interaction Problems 1 Introduction 2 The Nonlinear Problem 3 Discretization and Linearization 3.1 Linearization with Newton Iteration 4 Newton Iteration and Low-Rank Methods 4.1 The Matrix Equation 4.2 Low-Rank Methods 5 Numerical Results 5.1 Parameters 5.2 Comparison ChebyshevT with Standard Newton Preconditioner and Eigenvalue Estimation 6 Conclusions References Simulating Two-Dimensional Viscoelastic Fluid Flows by Means of the ``Tensor Diffusion'' Approach 1 Introduction 2 The ``Tensor Diffusion'' Approach 3 Proof of Concept 3.1 Fully Developed Channel Flows for UCM 3.2 Poiseuille-Like Flow for the Wagner Model 4 Complex Flow Configurations 5 Conclusion References Dynamic and Weighted Stabilizations of the L-scheme Applied to a Phase-Field Model for Fracture Propagation 1 Introduction 2 The Phase-Field Fracture Model 3 The L-scheme with Dynamic Updates of the Stabilization Parameters 4 Numerical Tests References Adaptive Numerical Simulation of a Phase-Field Fracture Model in Mixed Form Tested on an L-shaped Specimen with High PoissonRatios 1 Introduction 2 A Phase-Field Model for Nearly Incompressible Solids 2.1 Notation and Spaces 2.2 Mixed Phase-Field Fracture Model 2.3 Numerical Treatment and Programming Code 2.4 Adaptive Refinement 3 Numerical Results 3.1 Configuration of the L-shaped Panel Test 4 Conclusion References Convergence Rates for Matrix P-Greedy Variants 1 Introduction 2 Approximation with Matrix-Valued Kernels 3 Matrix P-greedy Algorithms 4 Convergence Rates for k-Dimensional Greedy Space Extensions 5 Numerical Experiment References Efficient Solvers for Time-Periodic Parabolic Optimal Control Problems Using Two-Sided Bounds of Cost Functionals 1 Introduction 2 Time-Periodic Parabolic Optimal Control Problem 3 Two-Sided Bounds for the Optimal Control Problem 3.1 Guaranteed Upper Bound for the Cost Functional 3.2 Guaranteed Lower Bound for the Cost Functional 4 Multiharmonic Finite Element Discretization and the Preconditioned Minimal Residual Method 5 Numerical Results 6 Conclusions References Finite Element Approximation of a System Coupling Curve Evolution with Prescribed Normal Contact to a Fixed Boundary to Reaction-Diffusion on the Curve 1 Introduction 2 Weak Formulation and Finite Element Approximation 3 Numerical Results 3.1 Solution of the Discrete System (11) and (13) 3.2 Experimental Order of Convergence of (11) and (13) 3.3 Experimental Order of Convergence of the Coupled Scheme (11)–(13) References The Newmark Method and a Space–Time FEM for the Second–Order Wave Equation 1 Introduction 2 Stabilised Space–Time Finite Element Method 3 Newmark Galerkin Method 4 Comparison and Conclusions References A Mixed Dimensional Model for the Interaction of a Well with a Poroelastic Material 1 Introduction 2 The Mathematical Model 2.1 Three-Dimensional Model of a Well in a Deformable Material 2.2 Topological Model Reduction and Weak Formulation 3 Numerical Experiments References