Fast Boundary Element Methods in Engineering and Industrial Applications

Cover......Page 1
Front matter......Page 2
Introduction......Page 13
Basic Definitions......Page 15
Integral Transformations......Page 23
Fundamental Solution of the Helmholtz Equation......Page 26
Single-Layer and Double-Layer Potentials......Page 28
Sobolev Spaces on the Domain......Page 30
Sobolev Spaces on the Boundary......Page 33
Representation Formula......Page 38
Maxwell-Type Problems, Solution Spaces, and Trace Operators......Page 39
Asymptotic Conditions......Page 40
Representation Formula for Maxwell Solutions......Page 43
Jump Relations of the Layer Potentials......Page 54
Boundary Integral Operators......Page 57
Symmetry Properties......Page 59
Ellipticity Properties......Page 62
Calderón Projector for Interior and Exterior Problems......Page 65
Equivalent Maxwell-Type Problems, Dual Transformations......Page 67
Conclusions......Page 72
References\r......Page 73
Introduction......Page 75
Classical Derivation......Page 78
Differential Forms......Page 82
Dual Complex......Page 89
Derivative and Trace Operators......Page 90
Hodge Operators......Page 91
Discrete Equation......Page 92
Small Simplices......Page 93
Higher Order DEM......Page 96
Nonlinear Materials......Page 100
Numerical Results......Page 101
References......Page 103
Introduction......Page 105
Additive Schwarz Method for the hp-Version BEM for the Hypersingular Integral Equation on Rectangular Meshes\r......Page 108
Additive Schwarz Method for the p-Version BEM for the Hypersingular Integral Equation on Triangles\r......Page 112
Additive Schwarz Method for the hp-Version BEM for the Weakly Integral Equation\r......Page 118
References......Page 120
Introduction......Page 122
Boundary Integral Formulations for Transmission Problems......Page 123
Model Problem......Page 124
Steklov–Poincar´e Operator Interface Equation......Page 125
Single Layer Potential Formulation......Page 128
Double Layer Potential Formulation......Page 129
Evaluation of the Magnetic Field......Page 132
Boundary Element Methods......Page 135
Steklov–Poincar´e Operator Interface Equation......Page 136
Single Layer Potential Formulation......Page 138
Direct Double Layer Potential Formulation......Page 139
Indirect Double Layer Potential Formulation......Page 141
Sphere......Page 142
Cube......Page 143
Ring......Page 144
Ring with Gap......Page 149
Controllable Reactor......Page 150
References......Page 152
Introduction – State of the Art......Page 155
Time Dependent Boundary Integral Equations......Page 157
Governing Equations......Page 158
Integral Equations......Page 162
Convolution Quadrature......Page 165
Linear Multistep Based Convolution Quadrature......Page 166
Runge-Kutta Based Convolution Quadrature......Page 167
Implementation......Page 169
Convolution Quadrature Applied to Hyperbolic Initial Value Problems\r......Page 173
Bounds in the Laplace Domain......Page 174
Properties of Convolution Weights......Page 176
Dissipation and Dispersion......Page 178
Space Discretization......Page 179
Galerkin and Collocation in Space......Page 180
Fast Data-Sparse Methods in Frequency Domain......Page 181
Numerical Example......Page 182
References......Page 189
Introduction......Page 195
Heat Potentials as Abel Integral Operators......Page 197
Time Dependent Integral Operators......Page 199
Projection Methods......Page 200
Product Integration Methods......Page 201
Desingularized Quadrature......Page 202
The Fast Multipole Method in Time Domain......Page 203
Separation of Variables......Page 204
Hierarchy of Intervals......Page 205
Translation Operators......Page 207
The Standard FMM......Page 210
The Causal FMM......Page 211
Discretization of Thermal Layer Potentials......Page 213
Approximation Theory for the Heat Kernel......Page 215
Chebyshev Expansion of the Gauss Kernel......Page 216
Space-Time Subdivision......Page 219
Space-Time Translation Operators......Page 221
A Numerical Example......Page 224
References......Page 227
Introduction......Page 230
Governing Equations......Page 231
Integral Formulation......Page 232
Null Space Problem......Page 233
Extension to the Slip Flow Regime and Implementation......Page 234
Numerical Implementation......Page 235
Extension to High Frequency Oscillatory Flow......Page 239
Multipole Expansion......Page 241
Numerical Results......Page 245
References......Page 247
Introduction......Page 250
Steklov–Poincar´e Operator for 3D Linear Elastostatics......Page 253
Multibody Contact Problem without Friction......Page 254
Multibody Contact Problem with Tresca Friction......Page 257
TBETI Domain Decomposition......Page 258
Dual Formulation......Page 261
Preconditioning by the Projector to the Rigid Body Modes......Page 263
Optimality......Page 266
Demonstration of Scalability on Two Cantilever Beams in Mutual Contact\r......Page 269
Mechanical Engineering Problem: Yielding Clamp Connection\r......Page 271
References......Page 275