Numerical Mathematics and Advanced Applications ENUMATH 2019: European Conference, Egmond aan Zee, The Netherlands, September 30 - October 4

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