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Meshfree Methods for Partial Differential Equations III

:	Michael Griebel, Marc A. Schweitzer
:	Michael Griebel, Marc Alexander Schweitzer
:	Meshfree Methods for Partial Differential Equations III
:	Springer-Verlag
:	9783540462224
:	1
:	CHF 85.20
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	304
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

Meshfree methods for the numerical solution of partial differential equations are becoming more and more mainstream in many areas of applications. This volume represents the state-of-the-art in meshfree methods. It consists of articles which address the different meshfree techniques, their mathematical properties and their application in applied mathematics, physics and engineering.

	Preface	5
	Contents	6
	Local Maximum-Entropy Approximation Schemes	8
	1 Introduction	8
	2 Formulation	9
	3 Properties	17
	4 Other Interpretations: Relative Entropy	19
	5 Applications in Galerkin Methods	21
	6 Conclusions	22
	References	22
	Genetic Algorithms for Meshfree Numerical Integration	24
	1 Introduction	24
	2 Problem Formulation and Discretization	26
	3 Numerical Integration	37
	4 Numerical Examples	41
	5 Concluding Remarks	46
	References	46
	An RBF Meshless Method for Injection Molding Modelling	48
	1 Model Equations	48
	2 Pressure Field	50
	3 Front Displacement	56
	4 Conclusions	62
	References	62
	Strain Smoothing for Stabilization and Regularization of Galerkin Meshfree Methods	64
	1 Introduction	64
	2 Conforming Strain Smoothing for Rank Instability	65
	3 Additional Stabilization for Spurious Nonzero Energy Modes	69
	4 Gradient Strain Smoothing Regularization for Material Instability in Strain Localization	72
	5 Application to Fragment Penetration Problems	77
	6 Conclusions	80
	References	81
	Fuzzy Grid Method for Lagrangian Gas Dynamics Equations	83
	1 Smooth Particle Hydrodynamics	83
	2 Fuzzy Grid	85
	3 The Unsymmetrical Approach to Modify Weights	86
	4 The Symmetrical Approach to Modify Weights	87
	5 Numerical Examples	88
	6 Conclusion	92
	References	92
	New Shape Functions for Arbitrary Discontinuities without Additional Unknowns	93
	1 Introduction	93
	2 Level-Set Method	95
	3 Moving Least-Squares Method	95
	4 Design of Special Shape Functions	97
	5 Coupling	100
	6 Numerical Results	102
	7 Conclusion	107
	References	108
	A Meshless BEM for 2-D Stress Analysis in Linear Elastic FGMs	110
	1 Introduction	110
	2 Formulation of Boundary-Domain Integral Equations	112
	3 Transformation of Domain-Integrals into Boundary Integrals	114
	4 System of Linear Algebraic Equations	115
	5 Computation of Stresses	116
	6 Numerical Example	118
	7 Conclusions	122
	References	123
	A Particle-Partition of Unity Method Part VII: Adaptivity	125
	1 Introduction	125
	2 Partition of Unity Method	126
	3 Adaptive Multilevel Solution	133
	4 Numerical Results	142
	5 Concluding Remarks	150
	References	151
	Enriched Reproducing Kernel Particle Approximation for Simulating Problems Involving Moving Interfaces	152
	1 Introduction	152
	2 Enriched Functional Approximations	153
	3 Definition of the Continuous Shape Functions with Discontinuous Derivatives	159
	4 Enrichment Function Expressed by a Polynomial	161
	5 Numerical Results	163
	6 Conclusion	166
	References	166
	Deterministic Particle Methods for High Dimensional Fokker- Planck Equations	168
	1 A Polymer Model	168
	2 Meshfree Solution Methods	173
	3 QMC Product Measures	175
	4 QMC Simulations	181
	References	185
	Bridging Scale Method and Its Applications	187
	1 Bridging Scale Fundamentals	187
	2 Reduction of the MD Domain	192
	3 Cauchy-Born Rule	199
	4 Atomistic Model	200
	5 Dynamic Crack Propagation in Three Dimensions	200
	6 Discussion on the Bridging Scale Method	205
	References	206
	A New Stabilized Nodal Integration Approach	208
	1 Introduction	208
	2 Formulation	209
	3 Results	214
	4 Discussion	217
	References	218
	Multigrid and M-Matrices in the Finite Pointset Method for Incompressible Flows	219
	1 Introduction	219
	2 FPM for the Incompressible Navier-Stokes Equation	220
	3 Finite Difference Approximation	221
	4 Conditions for the Existence of Positive Stencils	224
	5 Optimization for Interior Points	228
	6 Setting Up the System Matrix	229
	7 Algebraic Multigrid	230
	8 Numerical Results	231
	9 Conclusions and Outlook	233
	References	234
	Assessment of Generalized Finite Elements in Nonlinear Analysis	235
	1 Introduction	235
	2 Formulation	236
	3 Numerical Examples	241
	4 Conclusion	246
	References	246
	A Meshfree Method for Simulations of Interactions between Fluids and Flexible Structures	248
	1 Introduction	248
	2 Governing Equations	249
	3 Numerical Schemes	251
	4 Numerical Examples	257
	5 Conclusion	261
	References	263
	Goal Oriented Error Estimation for the Element Free Galerkin Method	264
	1 Introduction	264
	2 Basics on Output Oriented Error Estimation in FEM	266
	3 Extension to Element Free Galerkin	269
	4 Numerical Results	274
	5 Concluding Remarks	279
	References	280
	Bubble and Hermite Natural Element Approximations	282
	1 Introduction	283
	2 Review of the Natural Element Method	284
	3 Hierarchical Bubble Functions in the Natural Element Method	286
	4 Hermite-Natural Element Formulation	292
	5 Conclusion	295
	References	296
	Color Plates	298