Numerical Mathematics and Advanced Applications (eBook)

Proceedings of ENUMATH 2005 the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005

Alfredo Bermúdez de Castro, Dolores Gómez, Peregrina Quintela, Pilar Salgado (Herausgeber)

eBook Download: PDF

2007 | 2006
XIX, 1232 Seiten
Springer Berlin (Verlag)
978-3-540-34288-5 (ISBN)

Infos

These proceedings collect lectures given at ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications held in Santiago de Compostela, Spain in July, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, and more.

Inhalt

Preface 5
Contents 7
PLENARY LECTURES 20
Compatible Discretizations in Two Dimensions 21
1 Introduction 21
2 Construction of the dual complex 23
3 Applications 30
References 37
Finite Element Approximation of the Three Field Formulation of the Elasticity Problem Using Stabilization 39
1 Introduction 39
2 Problem statement and Galerkin finite element discretization 41
3 Finite element approximation using subscales 42
4 Numerical analysis of the original formulation 45
5 A modified stabilized problem 49
6 Concluding remarks 54
References 55
Convergence of Adaptive Wavelet Methods for Goal– Oriented Error Estimation* 57
1 Introduction 57
2 Goal–oriented error estimation 59
3 Adaptive error estimation 64
4 Numerical experiments 72
References 77
Quadratic Programming and Scalable Algorithms for Variational Inequalities 80
1 Introduction 80
2 Bound constrained problems 81
3 Bound and equality constrained problems 83
4 Model problem 85
5 FETI and total FETI domain decomposition 87
6 FETI–DP domain decomposition and discretization 89
7 Numerical scalability 90
8 Numerical experiments 91
9 Comments and conclusions 93
Acknowledgements 93
References 93
Discontinuous Galerkin Methods for Friedrichs’ Systems 97
1 Introduction 97
2 Friedrichs’ systems 99
3 Design and analysis of DG methods 101
4 DG approximation of two-field Friedrichs’ systems 105
5 Examples 108
6 Concluding remarks 113
References 113
Highly Oscillatory Quadrature: The Story so Far 115
1 The challenge of high oscillation 115
2 Asymptotic expansion in the absence of critical points 117
3 Asymptotic, filon and levin methods 120
4 Critical points 129
5 Conclusions and pointers for further research 133
References 136
The 3D Inverse Electromagnetic Scattering Problem for a Coated Dielectric 137
1 Introduction 137
2 Formulation of the direct and inverse scattering problem 138
3 Analysis of the inverse problem 141
4 Numerical example 149
5 Conclusion 150
Acknowledgment 151
References 151
Functional Approach to Locally Based A Posteriori Error Estimates for Elliptic and Parabolic Problems 153
1 Introduction 153
2 Functional a posteriori estimates for elliptic problems 155
3 Functional a posteriori estimates for a model evolutionary problem 164
References 167
Finite Element Approximation of 2D Parabolic Optimal Design Problems 169
1 Introduction 169
2 Preliminaries 173
3 Preliminaries on the convergence of the numerical scheme 175
4 Convergence of discrete optimal shapes 179
5 Gradient calculations: A numerical approach 181
6 Conclusions 191
Acknowledgements 192
References 192
CONTRIBUTED LECTURES 195
3D Free Surface Flows Simulations Using a Multilayer Saint- Venant Model. Comparisons with Navier- Stokes Solutions 197
1 Introduction 197
2 Navier-Stokes equations and hydrostatic approximation 197
3 A Multilayer saint-venant system 199
4 Numerical method 201
5 Numerical results 202
References 204
Some Well-Balanced Shallow Water-Sediment Transport Models 206
1 Sediment transport model 206
2 Finite volume method for non conservative hyperbolic systems 209
3 High order schemes based on state reconstruction 211
4 Numerical test: comparison with an analytical solution 212
References 213
Highly Accurate Conservative Finite Difference Schemes and Adaptive Mesh Refinement Techniques for Hyperbolic Systems of Conservation Laws* 214
1 Introduction 214
2 Finite-difference Shu-Osher schemes 215
3 Adaptive mesh refinement for Shu-Osher schemes 217
4 Numerical examples 219
5 Conclusions 220
References 221
Finite Volume Solvers for the Shallow Water Equations Using Matrix Radial Basis Function Reconstruction 223
1 Finite volume methods for shallow water models 223
2 Matrix valued Radial Basis Functions for vector field reconstruction 225
3 Applications to environmental modelling 226
References 230
On Numerical Schemes for a Hierarchy of Kinetic Equations 232
1 Introduction 232
2 Hexagonal kinetic models 233
3 Hexagonal hierarchy 235
4 Coupling of two kinetic models 236
References 239
Computational Aspects of the Mesh Adaptation for the Time Marching Procedure 240
1 Euler equations 240
2 Adaptive algorithm 241
3 Anisotropic mesh adaptation 242
4 Geometric mass conservation law 244
5 Numerical example 246
Acknowledgement 247
References 247
On the Use of Slope Limiters for the Design of Recovery Based Error Indicators 248
1 Introduction 248
2 A posteriori error indication 249
3 Limited gradient averaging 250
4 Limited gradient reconstruction 251
5 Adaptation strategy 253
6 Numerical examples 254
7 Conclusions 254
References 255
On a Superconvergence Result for Mixed Approximation of Eigenvalue Problems 257
1 Introduction 257
2 Statement of the problem and its discretization 258
3 Main results 259
4 Numerical results 260
References 264
Comparative Study of the a Posteriori Error Estimators for the Stokes Problem 266
1 Introduction 266
2 The stokes problem and its approximation 267
3 Estimation of the deviation from the exact solution 268
4 Numerical experiments 269
References 273
Error Control for Discretizations of Electromagnetic- Mechanical Multifield Problem 274
1 Introduction 274
2 Electromagnetic forming 275
3 Error control for coupled and mixed problems 278
References 281
A Safeguarded Zienkiewicz-Zhu Estimator 283
1 Introduction 283
2 Error estimator and theoretical results 284
3 Numerical results 287
References 290
Some Remarks on a Model for the Atmospheric Pressure in Ocean Dynamics 292
1 Introduction 292
2 Modelling of non-hydrostatic free-surface flows 293
3 A linearised model for the free surface equation 296
References 299
Computational Time Improvement for Some Shallow Water Finite Volume Models Applying Parallelization and Optimized Small Matrix Computations. 301
1 Introduction 301
2 Equations 302
3 Numerical scheme 303
4 Parallel SIMD implementation 303
References 308
Discretization Error Estimates for an Optimal Control Problem in a Nonconvex Domain 311
1 Introduction 311
2 Theory 312
3 Numerical results 315
References 319
A Posteriori Estimates for Cost Functionals of Optimal Control Problems 320
1 Introduction 320
2 Majorants for the cost functional 322
3 Properties of majorants 323
4 Practical implementation 324
5 Numerical experiments 325
References 327
Optimization of a Duality Method for the Compressible Reynolds Equation 330
1 The mathematical model 330
2 Numerical solution 331
3 Optimization of the duality algorithm 333
4 Numerical examples 335
5 Conclusions 337
Aknowledgments 337
References 337
Time-Space & Space-Time Elements for Unsteady Advection- Dominated Problems
1 Introduction 339
2 Stabilization techniques for the stationary problem 340
3 Stabilized methods for the non-stationary problem 341
4 Numerical Experiments 345
Acknowledgements 346
References 346
On Discontinuity–Capturing Methods for Convection– Diffusion Equations 347
1 Introduction 347
2 Galerkin’s finite element discretization 348
3 The SUPG method 348
4 Methods diminishing spurious oscillations in layers 349
5 Conclusions 353
Acknowledgements 354
References 354
Algebraic Flux Correction for Finite Element Approximation of Transport Equations 356
1 Introduction 356
2 Flux decomposition 356
3 Algebraic flux correction 357
4 Numerical example 362
5 Conclusions 363
References 363
A Parallel Multiparametric Gauss-Seidel Method* 365
1 Introduction 365
2 The local modified extrapolated Gauss-Seidel ( LMEGS) method 366
3 The eigenvalue relationship 366
4 Determination of good values 368
5 Numerical results and conclusions 370
Acknowledgement 372
References 372
A Numerical Scheme for the Micro Scale Dissolution and Precipitation in Porous Media 373
1 Introduction 373
2 The numerical scheme 376
3 A fixed point iteration 377
4 A numerical example 379
Acknowledgment 379
References 380
Discrete Kinetic Methods for a Degenerate Parabolic Equation in Dimension Two. 383
1 Introduction 383
2 Kinetic models 384
3 The numerical schemes 386
4 Numerical experiments 389
References 390
Anisotropic Doubly Nonlinear Degenerate Parabolic Equations 391
1 Introduction 391
2 Entropy solution 392
3 Renormalized entropy solution 394
Acknowledgement 396
References 396
A Multiresolution Method for the Simulation of Sedimentation- Consolidation Processes 397
1 Introduction 397
2 The multiresolution scheme 398
3 Sedimentation-consolidation processes 402
4 Numerical results 402
Acknowledgements 404
References 404
Diffusive Relaxation Limit for Hyperbolic Systems 406
1 Introduction 406
2 BGK approximation of strongly parabolic systems 409
3 One–dimensional semilinear model in viscoelasticity 410
4 Multidimensional viscoelasticity and modulated energy 411
References 413
Parallel Algorithms for Nonlinear Diffusion by Using Relaxation Approximation 414
1 Relaxation approximation of nonlinear diffusion 414
2 The numerical scheme 415
3 Numerical results 417
4 Concluding remarks 421
References 421
On a Degenerated Parabolic-Hyperbolic Problem Arising From Stratigraphy 422
1 Introduction and presentation of the model 422
2 A locally hyperbolic behaviour 423
3 Definition of a solution and existence results for a discretized problem 424
4 Some numerical illustrations 428
5 Conclusion and open problems 428
References 429
Schwarz Domain Decomposition Preconditioners for Interior Penalty Approximations of Elliptic Problems 432
1 Introduction 432
2 Discontinuous Galerkin methods for elliptic problems 433
3 Non-overlapping Schwarz methods 434
4 Convergence analysis 436
5 Numerical results 437
References 439
Higher Order Semi-Implicit Discontinuous Galerkin Finite Element Schemes for Nonlinear Convection- Diffusion Problems* 441
1 Introduction 441
2 Scalar equation 442
3 Numerical results 446
4 Conclusion 448
References 448
On Some Aspects of the Discontinuous Galerkin Method* 449
1 Continuous problem 449
2 Discretization of the problem 450
3 Error estimates 453
4 Application of the DGFEM to compressible flow with a wide range of mach numbers 455
5 Conclusion 455
References 456
Mixed Discontinuous Galerkin Methods with Minimal Stabilization 457
1 DG methods 457
2 Minimal stabilization 460
3 Numerical results 462
References 464
Discontinuous Galerkin Finite Element Method for a Fourth- Order Nonlinear Elliptic Equation Related to the Two- Dimensional Navier– Stokes Equations 466
1 Introduction 466
2 Mathematical formulation 468
3 DGFEM for a 4th-order advective PDE 469
4 Numerical results 471
References 473
Fourier Method with Nitsche-Mortaring for the Poisson Equation in 3D 475
1 Introduction 475
2 Fourier decomposition and mortaring in 2D 477
3 Fourier-nitsche-finite-element approximation in 3D 479
References 481
Substructuring Preconditioners for the Bidomain Extracellular Potential Problem 483
1 Introduction 483
2 Mortar method 484
3 Substructuring preconditioners 485
References 490
A Face Penalty Method for the Three Fields Stokes Equation Arising from Oldroyd- B Viscoelastic Flows 493
1 Introduction 493
2 A finite element formulation 495
3 The inf-sup condition 496
4 A priori error estimates 496
5 A stable iterative algorithm 497
6 Preliminary numerical results 497
References 499
Anisotropic H1-Stable Projections on Quadrilateral Meshes 501
1 Introduction 501
2 Anisotropic H1-stable projectors 503
3 General result 508
References 509
Continuous Interior Penalty hp-Finite Element Methods for Transport Operators 510
1 Introduction 510
2 Continuous interior penalty finite element methods 511
3 Technical results 512
4 Convergence analysis 514
5 Numerical results 514
References 517
A Nonconforming Finite Element Method with Face Penalty for Advection– Diffusion Equations 518
1 Introduction 518
2 The nonconforming finite element scheme with face penalty 519
3 A posteriori error estimates 522
4 Numerical results 523
Acknowledgment 524
References 525
Efficient Multigrid and Data Structures for Edge- Oriented FEM Stabilization 526
1 Introduction 526
2 Sparsity of the matrix 527
3 Local pressure Schur complement approach 530
4 Numerical example 532
References 533
Adaptive Methods for Dynamical Micromagnetics 535
1 Introduction 535
2 Numerical methods 536
3 Adaptive algorithm 538
4 Numerical experiment 539
References 541
Stability for Walls in Ferromagnetic Nanowire 543
1 Model for ferromagnetic nanowires 543
2 Landau-Lifschitz Equation in the mobile frame 545
3 A new system of coordinates 546
4 Estimates for the perturbations 548
References 550
Continuous Galerkin Methods for Solving Maxwell Equations in 3D Geometries 551
1 Introduction and notations 551
2 Variational formulations and discretization 553
3 Numerical results and conclusion 555
References 558
On the Use of the Gautschi-Type Exponential Integrator for Wave Equations 560
1 Introduction 560
2 Sine–Gordon equation 561
3 Discretisation 562
4 The Gautschi-type exponential integrator 564
5 Numerical example 565
References 566
Positivity of Exponential Multistep Methods 567
1 Introduction 567
2 Analytical framework 568
3 Exponential multistep methods 570
4 Positivity and order barrier 571
References 574
Stability Results and Algorithmic Strategies for the Finite Element Approach to the Immersed Boundary Method 576
1 Introduction 576
2 The finite element immersed boundary method 577
3 Time discretization by finite differences 579
4 Stability analysis by energy estimates 580
5 Numerical results 581
6 Conclusions 583
References 583
A Comparison of Enthalpy and Temperature Methods for Melting Problems on Composite Domains 585
1 Introduction 585
2 Problem description 586
3 Numerical methods 588
4 Numerical experiments 590
5 Conclusions 592
References 592
Qualitative Properties of a Numerical Scheme for the Heat Equation 593
1 Introduction 593
2 Proof of the results 595
Acknowledgements 600
References 600
Modeling Radiation and Moisture Content in Fire Spread 601
1 Introduction 601
2 Physical model 602
3 Governing equations 602
4 Numerical method 604
5 Numerical results 607
Acknowledgement 608
References 608
Fast Multipole Method for Solving the Radiosity Equation 609
1 Introduction 609
2 Radiosity equation and numerical solution 610
3 FMM and kernel expansion 611
4 A new fast method 612
5 Numerical results 615
6 Conclusion 616
References 616
Numerical Modelling of Kinetic Equations 618
1 Introduction 618
2 Asymptotic method 619
3 Numerical examples 622
References 625
On a Subclass of H¨ older Continuous Functions with Applications to Signal Processing 627
1 Introduction 627
2 H¨ older continuous spaces 628
3 Generalized Harten’s Subcell resolution technique 630
4 Numerical experiments 631
Acknowledgments 634
References 634
Modelisation and Simulation of Static Grain Deep- Bed Drying 636
1 Introduction 636
2 Models 637
3 The numerical schemes 638
4 Numerical experiments and comparisons 642
References 643
Hybrid Godunov-Glimm Method for a Nonconservative Hyperbolic System with Kinetic Relations 644
1 Introduction 644
2 The PDE model and main properties 645
3 Godunov-Glimm Hybrid method 647
4 The nonlinear projection 649
References 651
Cell-Average Multiwavelets Based on Hermite Interpolation* 652
1 Introduction 652
2 Harten’s framework for multiresolution analysis 652
3 Vector multiresolution analysis for cell-averaged data 654
4 Numerical experiments 657
References 659
On a General Definition of the Godunov Method for Nonconservative Hyperbolic Systems. Application to Linear Balance Laws 660
1 Introduction 660
2 Choice of paths 662
3 Godunov’s method 664
4 Application to linear balance laws 665
Acknowledgements 667
References 667
Sequential Flux-Corrected Remapping for ALE Methods 669
1 Introduction 669
2 Sequential FCR method 671
3 Numerical examples 675
Acknowledgments 676
References 676
Orthogonal hp-FEM for Elliptic Problems Based on a Non- Affine Concept 679
1 Introduction and historical remarks 679
2 Preliminaries 680
3 Numerical example 681
4 Construction of basis functions 682
5 Numerical example continued 685
Acknowledgment 686
References 686
On Some Aspects of the hp-FEM for Time- Harmonic Maxwell’s Equations 687
1 Introduction 687
2 Formulation of the problem 688
3 Shape functions 689
4 Numerical experiments 692
5 Conclusion and outlook 692
Acknowledgment 694
References 694
Numerical Simulation of Phase-Transition Front Propagation in Thermoelastic Solids 697
1 Introduction 697
2 Formulation of the problem 698
3 Conservative wave propagation algorithm 699
4 Contact quantities and numerical fluxes 701
5 Conclusions 703
Acknowledgment 704
References 704
The Level Set Method for Solid-Solid Phase Transformations 706
1 Introduction 706
2 The physical problem 708
3 The computational method 709
4 Numerical results 710
5 Conclusions 712
References 713
A Non-Monotone Fast Marching Scheme for a Hamilton- Jacobi Equation Modelling Dislocation Dynamics* 715
1 Introduction 715
2 The FMM algorithm for unsigned velocity 717
3 Numerical tests 719
Acknowledgments 722
References 722
A Time–Adaptive Semi–Lagrangian Approximation to Mean Curvature Motion 724
1 Introduction 724
2 General requirements on the adaptation strategy for geometric equations 726
3 A strategy based on local truncation error 727
4 Numerical tests 729
References 731
Heterogeneous Multiscale Methods with Quadrilateral Finite Elements 733
1 Introduction 733
2 HMM with quadrilaterals finite elements 734
3 Error analysis 736
4 Numerical experiments 738
Acknowledgment 739
References 740
Stabilizing the P1/P0 Element for the Stokes Problem via Multiscale Enrichment 742
1 Introduction 742
2 The model problem and the general framework 743
3 Application to the 745
pair 745
4 Numerical validations 748
References 749
Adaptive Multiresolution Methods for the Simulation of Shocks/ Shear Layer Interaction in Confined Flows 751
1 Introduction 751
2 Numerical results 752
3 Conclusion and perspectives 756
References 758
Local Projection Stabilization for the Stokes System on Anisotropic Quadrilateral Meshes 760
1 Introduction 760
2 Local projection stabilization on isotropic meshes 761
3 Anisotropic affine linear meshes 762
4 Local projection stabilization on anisotropic meshes 764
References 767
An Interior Penalty Variational Multiscale Method for High Reynolds Number Flows 769
1 Introduction 769
2 The equations of incompressible flow 770
3 Separation of scales and stabilized finite element methods 770
4 A posteriori error estimation 774
5 A numerical result 775
References 775
Variational Multiscale Large Eddy Simulation of Turbulent Flows Using a Two- Grid Finite Element or Finite Volume Method 778
1 Introduction 778
2 Multiscale formulation 779
3 Numerical results for turbulent flow in a diffuser 782
4 Conclusions 784
Acknowledgements 785
References 785
Issues for a Mathematical Definition of LES 786
1 Introduction 786
2 Suitable approximations 788
3 Review of existing pre–LES–models 789
4 Discretization 791
References 793
Stabilized FEM with Anisotropic Mesh Refinement for the Oseen Problem 795
1 Introduction 795
2 Stabilized FEM for linearized Navier-Stokes problem 796
3 Stability and convergence on hybrid meshes 798
4 Error estimates and design of stabilization parameters 799
5 Application to channel flow 801
Acknowledgment 802
References 802
Semi-Implicit Multiresolution for Multiphase Flows 804
1 Introduction 804
2 Semi implicit scheme on uniform grid 806
3 Multiscale analysis of the explicit-implicit scheme 807
References 811
Numerical Simulation of Vortex-Dipole Wall Interactions Using an Adaptive Wavelet Discretization with Volume Penalisation 812
1 Introduction 812
2 Adaptive wavelet discretization with volume penalisation 813
3 Vortex-dipole wall interactions 816
4 Conclusions 818
Acknowledgements 819
References 819
Inviscid Flow on Moving Grids with Multiscale Space and Time Adaptivity 821
1 Introduction 821
2 The ALE formulation of the Euler equations 822
3 Finite volume discretization 823
4 Adaptive multiscale method 825
5 Numerical results 827
References 828
A Relaxation Method for a Two Phase Flow with Surface Tension 831
1 Introduction 831
2 Numerical approximation 833
3 Relaxation method for the simplified model with surface tension forces 834
4 Numerical results 837
5 Conclusion 838
References 838
Extension of Interface Coupling to General Lagrangian Systems 840
1 Introduction 840
2 Coupling two p- systems 843
3 Coupling two Euler systems in Lagrangian coordinates 844
4 Coupling Lagrangian systems of different dimensions 846
5 Conclusion 847
References 847
A Numerical Scheme for the Modeling of Condensation and Flash Vaporization in Compressible Multi- Phase Flows 849
1 Introduction 849
2 The thermodynamics of phase transition 849
3 The Riemann problem with phase transition at equilibrium 850
4 The Riemann problem with out of equilibrium EOS 852
5 Numerical scheme 854
6 Numerical results 854
7 Conclusions 856
Acknowledgments 856
References 856
An Adaptive Operator Splitting of Higher Order for the Navier- Stokes Equations 858
1 Introduction 858
2 The Taylor based gradient recovery technique 859
3 The stabilized base splitting 860
4 The multi-grid postprocessing 861
5 Numerical results 862
6 Conclusions 865
Acknowledgment 865
References 865
The POD Technique for Computing Bifurcation Diagrams: A Comparison among Different Models in Fluids 867
1 Introduction 867
2 The POD technique 868
3 Description of the examples 870
4 Computation of the bifurcation diagrams of the example models 872
5 Conclusions 873
Acknowledgement 874
References 874
Filtering of Singularities in a Marangoni Convection Problem 876
1 Introduction 876
2 Formulation of the problem 877
3 Basic state 878
4 Linear stability 880
5 Conclusions 883
Acknowledgments 883
References 883
On Application of Stabilized Higher Order Finite Element Method on Unsteady Incompressible Flow Problems 884
1 Mathematical model 884
2 Time-spatial discretization 887
3 Numerical solution and results 889
References 891
Numerical Simulation of Coupled Fluid-Solid Systems by Fictitious Boundary and Grid Deformation Methods 893
1 Introduction 893
2 Grid deformation method 895
3 Numerical solution of the fluid-solid system 896
4 Verification of the numerical techniques 898
5 Conclusions 899
References 900
An Iterative Method for Solving Non-Linear Hydromagnetic Equations 903
1 Introduction. Statement of the problem 903
2 An iterative method for the magnetostatic system 905
3 Finite element discretization 906
4 Computational tests 909
References 910
Mathematical and Numerical Analysis of a Class of Non- linear Elliptic Equations in the Two Dimensional Case 912
1 Introduction 912
2 Statement of the main result 913
3 Proof of theorem 1 914
4 Numerical method 916
References 919
A s-step Variant of the Double Orthogonal Series Algorithm 922
1 Introduction 922
2 The algorithm of the Double Orthogonal Series 923
3 s-Step methods 924
4 The s-step variant of the double orthogonal series 924
5 Numerical results 926
6 Conclusions 929
Acknowledgment 929
References 929
Linear Equations in Quaternions 930
1 Basic properties and definitions for quaternions 930
2 Linear equations in quaternions 932
Acknowledgment 937
References 937
Computing the Analytic Singular Value Decomposition via a Pathfollowing 939
1 Introduction 939
2 Formulation of the problem 940
3 Solving defining equations 942
4 Experiments 943
5 Conclusions 945
Acknowledgments 946
References 946
A Jacobi-Davidson Method for Computing Partial Generalized Real Schur Forms 948
1 Introduction 948
2 The RJDQZ method for real matrix pencils 949
3 Numerical comparison 953
4 Conclusions 955
References 955
Pricing Multi-Asset Options with Sparse Grids and Fourth Order Finite Differences 958
1 Introduction 958
2 Model 958
3 Discretization 959
4 Sparse grid combination technique 961
5 Numerical results 963
6 Conclusions 965
References 965
A Third Order Linearly Implicit Fractional Step Method for Semilinear Parabolic Problems 968
1 Introduction 968
2 A new third order linearly implicit FSRK method 970
3 Numerical tests 973
References 976
Numerical Solution of Optimal Control Problems with Sparse SQP- Methods 977
1 Introduction 977
2 Optimal control problem 978
3 SQP-methods 979
4 Equality constrained quadratic subproblem 980
5 Approximation of the Hessian 981
6 Example 982
References 984
Semi-Deterministic Recursive Optimization Methods for Multichannel Optical Filters 986
1 Introduction 986
2 Global optimization methods 987
3 Application to multichannel optical filters design 990
4 Conclusions 993
References 993
A Multigrid Method for Coupled Optimal Topology and Shape Design in Nonlinear Magnetostatics* 994
1 Introduction 994
2 Topology optimization for magnetostatics 995
3 Sequential coupling of topology and shape optimization 997
4 Multilevel shape optimization 997
5 Numerical results 999
6 Conclusion 1000
References 1001
Nonsmooth Optimization of Eigenvalues in Topology Optimization 1002
1 Introduction 1002
2 Topology optimization and eigenproblems 1003
3 Nonsmooth analysis 1005
4 Numerical results 1007
5 Conclusion 1009
References 1009
Derivative Free Optimization of Stirrer Configurations 1010
1 Introduction 1010
2 Flow solver and numerical optimization tool 1011
3 Results 1013
4 Conclusion 1016
Acknowledgment 1017
References 1017
Mathematical Modelling and Numerical Optimization in the Process of River Pollution Control 1019
1 Introduction 1019
2 Mathematical formulation 1020
3 Numerical solution 1022
4 Numerical results 1025
Acknowledgements 1026
References 1026
A Family of C0 Finite Elements for Kirchhoff Plates with Free Boundary Conditions 1029
1 Introduction 1029
2 Kirchhoff plate bending problem 1030
3 Finite element formulation 1031
4 A-priori error estimates 1032
5 A-posteriori error estimates 1033
6 Computational results 1034
References 1036
A Postprocessing Method for the MITC Plate Elements 1037
1 Introduction 1037
2 The Reissner–Mindlin plate model 1037
3 MITC finite element methods 1038
4 Superconvergence 1039
5 Postprocessing method 1040
6 Benchmark computations 1041
References 1045
A Uniformly Stable Finite Difference Space Semi- Discretization for the Internal Stabilization of the Plate Equation in a Square 1046
1 Statement of the main result 1046
2 Proof of Theorem 1 1048
References 1053
An e-Uniform Hybrid Scheme for Singularly Perturbed 1- D Reaction- Diffusion Problems 1056
1 Introduction 1056
2 The cubic spline-cum-finite difference scheme 1057
3 Uniform convergence analysis on a Shishkin mesh 1059
4 Numerical experiments 1062
5 Conclusions 1062
References 1063
A Dynamic Frictional Contact Problem of a Viscoelastic Beam 1066
1 Introduction 1066
2 The variational formulation 1067
3 Numerical approximation 1068
4 Numerical results 1070
Acknowledgements 1072
References 1073
Numerical Analysis of a Frictional Contact Problem for Viscoelastic Materials with Long- Term Memory 1074
1 Introduction 1074
2 The model and its well-posedness 1075
3 Fully discrete approximation 1078
4 Numerical simulations 1079
Acknowledgments 1081
References 1081
A Suitable Numerical Algorithm for the Simulation of the Butt Curl Deformation of an Aluminium Slab 1083
1 Introduction 1083
2 Mathematical model 1084
3 Weak formulation 1085
4 Numerical solution 1086
5 Numerical results 1089
References 1091
An Efficient Solution Algorithm for Elastoplasticity and its First Implementation Towards Uniform h- and p- Mesh Refinements 1092
1 Introduction 1092
2 The Model of Elastoplasticity 1093
3 The algorithm 1095
4 Numerical experiments 1097
5 Conclusions and future work 1098
Acknowledgment 1098
References 1099
A LDG-BEM Coupling for a Class of Nonlinear Exterior Transmission Problems 1102
1 Introduction 1102
2 An exterior transmission problem 1103
3 LDG-BEM coupling 1105
Acknowledgements 1108
References 1109
High Order Boundary Integral Methods for Maxwell’s Equations: Coupling of Microlocal Discretization and Fast Multipole Methods 1110
1 Introduction 1110
2 The integral equations of Despr ´ es (EID) and MLFMM 1111
3 Finite elements of higher order and MLFMM 1112
4 Microlocal discretization (MD) and MLFMM 1113
5 Numerical results 1115
6 Conclusion 1117
References 1117
Indirect Methods with Brakhage–Werner Potentials for Helmholtz Transmission Problems 1119
1 Problem 1119
2 Boundary integral formulation 1120
3 Petrov–Galerkin methods 1122
4 Numerical approximation in two dimensions 1123
5 A numerical example 1125
Acknowledgements 1126
References 1126
A FEM–BEM Formulation for a Time– Dependent Eddy Current Problem 1128
1 Introduction 1128
2 Model problem 1129
3 Semi–discrete problem 1134
References 1136
Mixed Boundary Element–Finite Volume Methods for Thermohydrodynamic Lubrication Problems* 1137
1 Introduction 1137
2 Thermohydrodynamic mathematical model 1138
3 Numerical solution of hydrodynamic and fluid thermal models 1141
4 Numerical solution in the bush and the shaft 1142
5 Numerical solution of the global problem 1142
6 Extension to the evolution problem 1143
References 1144
Numerical Modelling for Leaching of Pesticides in Soils Modified by a Cationic Surfactant 1147
1 Introduction 1147
2 Laboratory experiments 1148
3 Models describing leaching of solutes in soils 1149
4 Numerical methods 1150
5 Parameter adjustment 1152
6 Examples 1153
Acknowledgement 1153
References 1154
Formulation of Mixed-Hybrid FE Model of Flow in Fractured Porous Medium* 1156
1 Rock Massif environment 1156
2 Linear steady Darcy’s flow 1158
3 Mathematical formulation of the problem 1158
4 Mixed-hybrid formulation 1159
5 Finite element approximation 1162
6 Conclusions 1163
References 1163
Newton–Type Methods for the Mixed Finite Element Discretization of Some Degenerate Parabolic Equations 1164
1 Introduction 1164
2 The fully discrete problem 1165
3 The Newton scheme 1167
4 Conclusions 1171
References 1171
Domain Decomposition Methods for Wave Propagation in Heterogeneous Media 1174
1 Formulation of the problem 1174
2 Time discretization 1176
3 Fully discrete scheme 1177
4 Energy inequality 1179
5 Numerical experiments 1180
References 1181
Galbrun’s Equation Solved by a First Order Characteristics Method 1183
1 Galbrun’s equation 1183
2 Characteristic curves 1186
3 Numerical approximation 1187
Acknowledgment 1190
References 1190
Open Subsystems of Conservative Systems 1191
1 Overview 1191
2 Open systems within conservative extensions 1193
3 Discussion 1198
References 1198
Author Index 1199

Produkt-Details

• Erscheint lt. Verlag: 8.10.2007
• Zusatzinfo: XIX, 1232 p. 300 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Mechanics • Numerical analysis • numerical simulation • Optimization • Partial differential equations • Simulation
• ISBN-10: 3-540-34288-5 / 3540342885
• ISBN-13: 978-3-540-34288-5 / 9783540342885