Meshfree methods for partial differential equations IX

Preface......Page 6
Contents......Page 7
 1 Introduction......Page 9
 2 Model Problem......Page 10
 3 GFEM and GFEMgl Approximations......Page 11
  3.2 Stable GFEM and Stable GFEMgl......Page 13
  4.1 Block Gauss-Seidel Algorithm......Page 14
   4.2.1 Block Jacobi Preconditioner......Page 15
   4.2.2 Block Gauss-Seidel Preconditioner......Page 16
 5 Analysis of a 3-D Edge-Crack......Page 17
  5.1 Condition Number Analysis......Page 18
  5.2 Performance of Preconditioners for GFEMgl and SGFEMgl......Page 20
  5.3 Comparison of BGS-PCG with Pardiso......Page 21
  5.4 Condition Number with Face Dirichlet Boundary Conditions......Page 22
 References......Page 23
 1 Introduction......Page 26
 2 The Method of Fundamental Solutions with Near-Boundary Sources......Page 29
   2.1.1 Accuracy......Page 31
   2.1.2 Condition Number......Page 32
   2.1.3 Convergence......Page 33
   2.1.4 Controlling by External Boundary Values......Page 34
  2.2 Band-Limited Approximation: A Two-Level Technique......Page 35
  2.3 Band-Limited Approximation: Extension to Multi-Level Method......Page 37
  2.4 Approximation by Near-Boundary Point Sources......Page 38
   2.4.1 Condition Number......Page 41
  2.5 Definition of Sources Using Quadtrees......Page 42
 3 A Numerical Example......Page 45
 References......Page 48
 1 Introduction......Page 50
 2 De-homogenization of the Homogenous Strain State......Page 53
 3 Classical Convergence of the Laminate Solution (Primarily a Finite Element Solution)......Page 54
 4 The Use of the Critical Properties to Write the MOS......Page 55
  4.2 Implementing the Critical Properties into the MOS Process......Page 56
 6 Concluding Remarks......Page 57
 References......Page 58
 1 Introduction......Page 59
 2 Parametric Partial Differential Equations......Page 63
  3.1 Taylor Spaces and Power Series Kernels......Page 65
 4 Sparse Grids......Page 67
 5 Error Estimates......Page 68
 6 Concluding Remarks and Future Work......Page 75
 References......Page 76
 1 Introduction......Page 78
  2.1 Point Cloud......Page 79
   2.2.1 Generalized Finite Difference Operators......Page 80
   2.2.2 Least Squares for Operator Generation......Page 82
   2.2.3 Solving PDEs on a GFDM-Basis......Page 84
   2.3.2 Reduction of Function Values by Integration......Page 85
  3.1 Pressure–Velocity Coupling......Page 86
   3.1.1 Surface–Surface Coupling......Page 87
   3.1.2 Volume–Volume Coupling......Page 88
  3.2 Velocity–Pressure Coupling......Page 90
  4.1 Water–Air Coupling in Pelton Turbines......Page 91
  4.2 Flow in Flexible Structures......Page 95
 References......Page 96
Parallel Detection of Subsystems in Linear Systems Arising in the MESHFREE Finite Pointset Method......Page 98
 2 Components......Page 99
  2.1 Graph Theory Basics and Notation......Page 100
  2.2 Related Work......Page 103
   2.3.1 The Geometric Case......Page 104
  2.4 Detecting Components in Parallel......Page 106
  2.5 Complexity of the Algorithm......Page 110
  2.6 Dealing with Components in the Linear Solver......Page 113
   2.7.1 The Valve Case......Page 114
 3 Avoiding Redistribution......Page 118
 References......Page 119
 1 Introduction......Page 121
  2.1 Problem Formulation......Page 122
  2.2 Level Set Method......Page 123
  2.3 Discretization in Time......Page 124
  3.1 Kernel Interpolation and Operator Approximation......Page 125
 4 Numerical Results......Page 128
  4.1 Example 1......Page 129
  4.3 Example 3......Page 131
  4.4 Example 4......Page 132
  4.5 Example 5......Page 135
 5 Conclusion......Page 136
 References......Page 137
 1 Introduction......Page 139
  2.1 Continuous Lippmann–Schwinger Equation......Page 141
   2.2.1 Training Stage......Page 142
   2.2.2 Prediction Stage......Page 143
   2.2.3 Summary......Page 144
  3.1 Macroscale Damage......Page 145
  3.2 Microscale Damage......Page 146
 4 Multiscale Carbon Fiber Reinforced Polymer Composite Cutting Process Modeling......Page 147
 References......Page 151
 1 Introduction......Page 153
 2 Preliminaries......Page 155
  3.1 Meshfree Approximation and Discretization......Page 158
  3.2 Semi-discrete Equations......Page 160
  4.1 The Adaptive Anisotropic Lagrangian Kernel for Large Deformation Analysis......Page 162
  4.2 The Bond-Based Failure Criterion for Material Separation Analysis......Page 163
 5 Numerical Example......Page 164
 References......Page 168
 1 Introduction......Page 171
  2.1 Partition of Unity Method......Page 173
  2.2 Numerical Enrichment Functions......Page 174
 3 Model Problem and Global-Local Formulation......Page 175
 4 Numerical Results......Page 178
 References......Page 185
 1 Introduction......Page 188
 2 Partition of Unity Method......Page 189
 3 FT-PUM for the Schrödinger Eigenproblem......Page 191
  3.1 Transformation on a Triclinic Unit Cell......Page 192
 4 Numerical Results......Page 194
 5 Concluding Remarks......Page 197
 References......Page 198
Editorial Policy......Page 199
Lecture Notesin Computational Scienceand Engineering......Page 201
Texts in Computational Scienceand Engineering......Page 207