Kunisch / Of / Steinbach Numerical Mathematics and Advanced Applications

Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007
1. Auflage 2008
ISBN: 978-3-540-69777-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 825 Seiten

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10-14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.

Autoren/Hrsg.

Kunisch, Karl

Of, Günther

Steinbach, Olaf

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;Plenary Lectures;16
3.1;The Worst Scenario Method: A Red Thread Running Through Various Approaches to Problems with Uncertain Input Data;17
3.2;Boundary and Finite Element Domain Decomposition Methods;29
3.3;Discontinuous Galerkin Elements for Reissner- Mindlin Plates;41
4;Contributed Lectures;51
5;A Posteriori Error Estimation and Adaptive Methods;52
5.1;Functional Type A Posteriori Error Estimates for Maxwell’s Equations;53
5.2;Space–Time Adaption for Advection- Diffusion- Reaction Problems on Anisotropic Meshes;61
5.3;A Posteriori Error Analysis for Kirchhoff Plate Elements;69
5.4;Adaptive Finite Element Simulation of Relaxed Models for Liquid- Solid Phase Transition;77
6;Biomedical Applications;85
6.1;A Numerical Study of the Interaction of Blood Flow and Drug Release from Cardiovascular Stents;86
6.2;Numerical Modelling of Epidermal Wound Healing;94
6.3;Model of Multiple Lexicographical Programming Applied in Cervical Cancer Screening;102
6.4;A Finite Element Model for Bone Ingrowth into a Prosthesis;110
7;Computational Electromagnetism;118
7.1;Space and Time Adaptive Calculation of Transient 3D Magnetic Fields;119
7.2;A Boundary Integral Formulation for Nonlocal Electrostatics;127
8;Computational Methods, Preconditioners, Solvers;135
8.1;Efficient Solution of Algebraic Bernoulli Equations Using H -Matrix Arithmetic;136
8.2;A Purely Algebraic Approach to Preconditioning Based on Hierarchical LU Factorizations;144
8.3;Additive Schwarz Preconditioners for Degenerate Problems with Isotropic Coefficients;152
8.4;Performance Analysis of Parallel Algebraic Preconditioners for Solving the RANS Equations Using Fluctuation Splitting Schemes;160
8.5;On Least-Squares Approximate Inverse-Based Preconditioners;168
8.6;On the Construction of Stable B-Spline Wavelet Bases;176
8.7;The Performance of a Multigrid Algorithm for the Acoustic Single Layer Equation;184
8.8;Constraints Coefficients in hp-FEM;192
8.9;A Boundary Element Algorithm for the Dirichlet Eigenvalue Problem of the Laplace Operator;200
8.10;On Efficient Solution of Linear Systems Arisingin hp-FEM;208
9;Convection, Diffusion, Conservation, and Hyperbolic Systems;216
9.1;Coupling Two Scalar Conservation Laws via Dafermos’ Self- Similar Regularization;217
9.2;A Sharp Interface and Fully Conservative Scheme for Computing Nonclassical Shocks;225
9.3;A Numerical Descent Method for an Inverse Problem of a Scalar Conservation Law Modelling Sedimentation;233
9.4;PSI Solution of Convection-Diffusion Equationswith Data in L;241
9.5;High Order Two Dimensional Numerical Schemes for the Coupling of Transport Equations and ShallowWater Equations;249
9.6;Well-Balanced High-Order MUSTA Schemes for Non- Conservative Hyperbolic Systems;257
9.7;Local Time Stepping for Implicit-Explicit Methods on Time Varying Grids;265
9.8;A ‘TVD-like’ Scheme for Conservation Laws with Source Terms;273
9.9;Application of the WAF Method to Shallow Water Equations with Pollutant and Non- Constant Bottom;281
9.10;A Third Order Method for Convection-Diffusion Equations with a Delay Term;289
9.11;A Third Order WLSQR Scheme on Unstructured Meshes with Curvilinear Boundaries;297
9.12;On the Choice of Parameters in Stabilization Methods for Convection– Diffusion Equations;305
9.13;On Path-Conservative Numerical Schemes for Hyperbolic Systems of Balance Laws;313
10;Discontinuous Galerkin Methods;321
10.1;An Augmented DG Scheme for Porous Media Equations;322
10.2;A Remark to the DGFEM for Nonlinear Convection- Diffusion Problems Applied on Nonconforming Meshes;330
10.3;BDF-DGFE Method for the Compressible Navier- Stokes Equations;338
10.4;Discontinuous Galerkin Method for the Numerical Solution of Inviscid and Viscous Compressible Flow;346
10.5;Numerical Integration in the Discontinuous Galerkin Method for Nonlinear Convection- Diffusion Problems in 3D;354
10.6;Implicit-Explicit Runge-Kutta Discontinuous Galerkin Finite Element Method for Convection- Diffusion Problems;362
11;Domain Decomposition Methods;370
11.1;A Domain Decomposition Method Derived from the Primal Hybrid Formulation for 2nd Order Elliptic Problems;371
11.2;A Posteriori Error Analysis of Penalty Domain Decomposition Methods for Linear Elliptic Problems;379
11.3;BETI-DP Methods in Unbounded Domains;387
11.4;Domain Decomposition and Model Reduction of Systems with Local Nonlinearities;395
11.5;An Adaptive Discontinuous Galerkin Scheme for Second Order Problems with an Interface;403
12;Finance, Stochastic Applications;411
12.1;Abstract Sensitivity Analysis for Nonlinear Equations and Applications;412
12.2;Multiscale Analysis for Jump Processes in Finance;420
13;Fluid Mechanics;428
13.1;A Hybrid Numerical Scheme for Aerosol Dynamics;429
13.2;Numerical Study of Mixed Finite Element and Multi Point Flux Approximation of Flow in Porous Media;437
13.3;Local Projection Stabilization for the Oseen System on Anisotropic Cartesian Meshes;445
13.4;Simulations of 3D Dynamics of Microdroplets: A Comparison of Rectangular and Cylindrical Channels;453
13.5;Incomplete Interior Penalty Galerkin Method for a Nonlinear Convection- Diffusion Equation;461
13.6;Numerical Simulations of Incompressible Laminar Flow for Newtonian and Non- Newtonian Fluids;469
13.7;Numerical Solution of 2D and 3D Unsteady Viscous Flows;477
13.8;Local Projection Stabilization of Finite Element Methods for Incompressible Flows;485
13.9;A Numerical Study of Local Projection Stabilisations Applied to Oseen Problems;493
13.10;Involutive Completion to Avoid LBB Condition;501
13.11;Numerical Computation of Unsteady Compressible Flows with Very Low Mach Numbers;509
13.12;A Mixed Hybrid Finite Element Discretization Scheme for Reactive Transport in Porous Media;517
13.13;Applying Local Projection Stabilization to inf- sup Stable Elements;525
13.14;Calibration of Model and Discretization Parameters for Turbulent Channel Flow;533
14;Fluid-Structure Interaction;541
14.1;Numerical Solution of Transonic and Supersonic 2D and 3D Fluid– Elastic Structure Interaction Problems;542
14.2;Numerical Simulations of Flow Induced Vibrations of a Profile;550
14.3;A Semi-Implicit Algorithm Based on the Augmented Lagrangian Method for Fluid- Structure Interaction;558
14.4;Automated Multi-Level Substructuring for a Fluid- Solid Vibration Problem;566
14.5;On Numerical Approximation of Fluid- Structure Interaction Problems;574
15;Optimal Control Problems;582
15.1;Fishways Design: An Application of the Optimal Control Theory;583
15.2;Moving Domain by Galerkin-Level Set Strategy: Application to Shape Geodesics;591
15.3;Numerical Analysis of a Control and State Constrained Elliptic Control Problem with Piecewise Constant Control Approximations;599
15.4;Globalization of Nonsmooth Newton Methods for Optimal Control Problems;607
15.5;An Inexact Trust-Region SQP Method with Applications to PDE- Constrained Optimization;615
15.6;Semi–Monotonic Augmented Lagrangians for Optimal Control and Parameter Identification;623
15.7;An Optimal Control Problem for Stochastic Linear PDE’s Driven by a Gaussian White Noise;631
15.8;A Priori Error Analysis for the Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems;639
15.9;A Priori Error Analysis for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems;647
15.10;Multigrid Methods for Linear Elliptic Optimal Control Problems;655
16;Optimization, Inverse Problems;663
16.1;An Active Curve Approach for Tomographic Reconstruction of Binary Radially Symmetric Objects;664
16.2;A Single-Pass Scheme for the Mean Curvature Motion of Convex Curves;672
16.3;A Semi-Lagrangian Approximation of Min– Max Type for the Stationary Mean Curvature Equation;680
16.4;Topological Derivative Based Methods for Non– Destructive Testing;688
16.5;A Characteristics Driven Fast Marching Method for the Eikonal Equation;696
16.6;Hierarchical Model Reduction for Advection- Diffusion- Reaction Problems;704
16.7;A Semi-Lagrangian Scheme for the Open Table Problem in Granular Matter Theory;712
16.8;On a Variational Approximation of the Effective Hamiltonian;720
16.9;Estimation of Diffusion Coefficients in a Scalar Ginzburg- Landau Equation by Using Model Reduction;728
16.10;Reduced Order Models (POD) for Calibration Problems in Finance;736
17;Ordinary Differential Equations;744
17.1;A Collocation Method for Quadratic Control Problems Governed by Ordinary Elliptic Differential Equations;745
17.2;A Road Traffic Model with Overtaking: Continuation of the Oscillatory Patterns;753
17.3;A Second Order Scheme for Solving Optimization- Constrained Differential Equations with Discontinuities;761
17.4;Optimal Load Changes for a Molten Carbonate Fuel Cell Model;769
17.5;Differential DAE Index for Reactive Euler Equations;777
17.6;Application of a First Order Asymptotic Method for Modeling Singularly Perturbed BVPs;785
18;Solid Mechanics;793
18.1;Newton-Like Solver for Elastoplastic Problems with Hardening and its Local Super- Linear Convergence;794
18.2;On a Fictitious Domain Method for Unilateral Problems;802
18.3;Bifurcations in Contact Problems with Local Coulomb Friction;810
18.4;Point Load on a Shell;818