| Description |
1 online resource (xiv, 277 pages) : illustrations |
| Series |
Numerical mathematics and scientific computation |
|
Numerical mathematics and scientific computation.
|
| Contents |
1 Introduction; 2 Optimal shape design; 2.1 Introduction; 2.2 Examples; 2.2.1 Minimum weight of structures; 2.2.2 Wing drag optimization; 2.2.3 Synthetic jets and riblets; 2.2.4 Stealth wings; 2.2.5 Optimal breakwater; 2.2.6 Two academic test cases: nozzle optimization; 2.3 Existence of solutions; 2.3.1 Topological optimization; 2.3.2 Suficient conditions for existence; 2.4 Solution by optimization methods; 2.4.1 Gradient methods; 2.4.2 Newton methods; 2.4.3 Constraints; 2.4.4 A constrained optimization algorithm; 2.5 Sensitivity analysis |
|
2.5.1 Sensitivity analysis for the nozzle problem2.5.2 Numerical tests with freefem++; 2.6 Discretization with triangular elements; 2.6.1 Sensitivity of the discrete problem; 2.7 Implementation and numerical issues; 2.7.1 Independence from the cost function; 2.7.2 Addition of geometrical constraints; 2.7.3 Automatic differentiation; 2.8 Optimal design for Navier-Stokes flows; 2.8.1 Optimal shape design for Stokes flows; 2.8.2 Optimal shape design for Navier-Stokes flows; References; 3 Partial differential equations for fluids; 3.1 Introduction; 3.2 The Navier-Stokes equations |
| Summary |
Examining shape optimization problems for fluids, with the equations needed for their understanding and the simulation of these problems, this text introduces automatic differentiation, approximate gradients, and automatic mesh refinement |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Fluid dynamics -- Mathematics
|
|
Mathematical optimization.
|
|
Shape theory (Topology)
|
|
TECHNOLOGY & ENGINEERING -- Structural.
|
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Fluid dynamics -- Mathematics
|
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Mathematical optimization
|
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Shape theory (Topology)
|
| Form |
Electronic book
|
| Author |
Pironneau, Olivier, author.
|
| ISBN |
9780199546909 |
|
0199546908 |
|
9780191574214 |
|
019157421X |
|
9780191720482 |
|
0191720488 |
|
9781523121236 |
|
1523121238 |
|
