Griebel / Schweitzer Meshfree Methods for Partial Differential Equations II

1. Auflage 2006
ISBN: 978-3-540-27099-7
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 43, 311 Seiten

Reihe: Lecture Notes in Computational Science and Engineering

Griebel (Eds), Meshfree Methods for Partial Differential Equations II (LNCSE 43)

Autoren/Hrsg.

Griebel, Michael

Schweitzer, Marc Alexander

Inhaltsverzeichnis

1;Preface;5
2;Contents;6
3;A Particle Strategy for Solving the Fokker- Planck Equation Modelling the Fiber Orientation Distribution in Steady Recirculating Flows Involving Short Fiber Suspensions;8
3.1;1 Introduction;8
3.2;2 A Particle Discretisation;11
3.3;3 Numerical Examples;17
3.4;4 Conclusions;21
3.5;References;22
4;Extended Meshfree Method for Elastic and Inelastic Media;24
4.1;1 Introduction;24
4.2;2 Review of Extended Meshfree Method;25
4.3;3 Extended Meshfree Method for Elastic Boundary Value Problems;30
4.4;4 Extended Meshfree Method for Inelastic Boundary Value Problems;35
4.5;5 Conclusions;42
4.6;6 Appendix;43
4.7;References;43
5;Meshfree Petrov-Galerkin Methods for the Incompressible Navier- Stokes Equations;46
5.1;1 Introduction;46
5.2;2 Stabilisation Schemes;47
5.3;3 The Stabilisation Parameter;49
5.4;4 Numerical Results;56
5.5;5 Conclusion;59
5.6;References;60
6;The a-shape Based Natural Element Method in Solid and Fluid Mechanics;62
6.1;1 Introduction;62
6.2;2 Natural Neighbour Galerkin Methods;63
6.3;3 Natural Element Methods for Incompressible Media;65
6.4;4 The a-shape based Natural Element Method;69
6.5;5 Numerical Examples;70
6.6;6 Closing Remarks;74
6.7;References;75
7;A Particle-Partition of Unity Method Part VI: A p- robust Multilevel Solver;78
7.1;1 Introduction;78
7.2;2 Partition of Unity Method;80
7.3;3 Multilevel Solution of Resulting Linear System;84
7.4;4 Numerical Results;94
7.5;5 Concluding Remarks;97
7.6;References;98
8;Enriched Reproducing Kernel Approximation: Reproducing Functions with Discontinuous Derivatives;100
8.1;1 Introduction;100
8.2;2 Enriched Reproducing Kernel Particle Approximation;102
8.3;3 The Case of a Function with Discontinuous Derivatives;104
8.4;4 Properties of the Moment Matrix;105
8.5;5 About the Resulting Shape Function and its Derivatives;107
8.6;6 Numerical Example;111
8.7;7 Conclusion;113
8.8;References;114
9;Reproducing Kernel Element Interpolation: Globally Conforming Im/ Cn/ Pk Hierarchies;116
9.1;1 Introduction;116
9.2;2 Reproducing Kernel Element Method;117
9.3;3 Globally Conforming Im/Cn/Pk Hierarchy I;122
9.4;4 Globally Conforming Im/Cn/Pk Hierarchy II;127
9.5;5 Numerical Examples;133
9.6;6 Closure;137
9.7;References;138
10;Multi-scale Analysis Using Two Influence Radii in EFGM;140
10.1;1 Introduction;140
10.2;2 P-like Adaptivity Analysis;142
10.3;3 Multi-Scale Analysis Using Two Nodal Points Layouts;144
10.4;4 Conclusion;154
10.5;References;154
11;Solution of a Dynamic Main Crack Interaction with a System of Micro- Cracks by the Element Free Galerkin Method;156
11.1;1 Introduction;156
11.2;2 The EFG Method for Dynamic Linear Elastic Fracture Mechanics;157
11.3;3 Solution of Multi-Crack Problems by the EFG Method;160
11.4;4 Individual Crack Subjected to Pulse Loading;164
11.5;5 Main Crack Propagation in a Field of Interacting Flaws under Dynamic Pulse Loading;168
11.6;6 Conclusions;173
11.7;References;174
12;Finite Cover Method for Physically and Geometrically Nonlinear Problems;176
12.1;1 Introduction;176
12.2;2 Finite Cover Method;177
12.3;3 Application to Evolution Problems of Failure Surfaces;182
12.4;4 Application to Finite Deformation Problems;189
12.5;5 Conclusion;194
12.6;References;196
13;A Numerical Scheme for Solving Incompressible and Low Mach Number Flows by the Finite Pointset Method;198
13.1;1 Introduction;198
13.2;2 Governing Equations;200
13.3;3 Numerical Scheme;201
13.4;4 Numerical Tests;207
13.5;References;212
14;SPH Renormalized Hybrid Methods for Conservation Laws: Applications to Free Surface Flows;214
14.1;1 Introduction;214
14.2;2 Classical Recipes;215
14.3;3 Weak Formulation;219
14.4;4 Application to Euler Equations;226
14.5;5 Applications;227
14.6;References;235
15;Discontinuous Radial Basis Function Approximations for Meshfree Methods;238
15.1;1 Introduction;238
15.2;2 Radial Basis Function Approximation;240
15.3;3 Approximation for Discontinuous Functions by Radial Basis Function Interpolation;241
15.4;4 Discrete Equations for Discontinuous Radial Basis Function Approximation;245
15.5;5 Example;247
15.6;6 Conclusions;256
15.7;References;258
16;Treating Moving Interfaces in Thermal Models with the C- NEM;262
16.1;1 Introduction;262
16.2;2 Problem Formulation;264
16.3;3 The Constrained Natural Element Method (C-NEM);265
16.4;4 C-NEM Discretization;269
16.5;5 Numerical Example;270
16.6;6 Conclusion;272
16.7;References;274
17;Bridging Scale Particle and Finite Element Methods;278
17.1;1 Introduction;278
17.2;2 Review of Multiscale Simulation Methods;280
17.3;3 Concurrent Bridging Scale Method;281
17.4;4 Bridging Scale Computations for Localized Failure;291
17.5;5 Conclusions;294
17.6;References;295
18;Color Plates;299