Slide 1 Oxford, June 1st, 2006 Nico Gauger and Andreas Griewank 3rd European Workshop on Automatic Differentiation Automated extension of fixed-point PDE solvers for optimal design with bounded retardation Nico Gauger 1),2) , Andreas Griewank 2) 1) DLR Braunschweig Institute of Aerodynamics and Flow Technology Numerical Methods Branch 2) Humboldt University Berlin Department of Mathematics
24
Embed
Automated extension of fixed-point PDE solvers for optimal ...
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Slide 1
Oxford, June 1st, 2006 Nico Gauger and Andreas Griewank3rd European Workshop on Automatic Differentiation
Automated extension of fixed-point PDE solversfor optimal design with bounded retardation
Nico Gauger1),2), Andreas Griewank2)
1) DLR BraunschweigInstitute of Aerodynamics and Flow TechnologyNumerical Methods Branch
2) Humboldt University BerlinDepartment of Mathematics
Slide 2
Oxford, June 1st, 2006 Nico Gauger and Andreas Griewank3rd European Workshop on Automatic Differentiation
CollaboratorsWith contributions to this talk:
• HU Berlin: J. Riehme
• Fastopt: R. Giering, Th. Kaminski
• TU Dresden: C. Moldenhauer, S. Schlenkrich,
A. Walther
FastOpt
Slide 3
Oxford, June 1st, 2006 Nico Gauger and Andreas Griewank3rd European Workshop on Automatic Differentiation
hybrid grids very complex configurationsgrid adaptation fully parallel softwareadjoint option
Slide 5
Oxford, June 1st, 2006 Nico Gauger and Andreas Griewank3rd European Workshop on Automatic Differentiation
Algorithmic Differentiation (AD)
Work in progress and results
• ADFLOWer generated with TAF (3D Navier-Stokes,k-w), first verifications and validation
• Adjoint version of TAUij (2D Euler) + mesh deformationand parameterization with ADOL-C, validated and tested
• First and second derivatives of a “FLOWer-Derivate”(2D Euler) + mesh deformation and parameterizationgenerated with TAPENADE, used for All-at-Once (Piggy-Back)
Slide 6
Oxford, June 1st, 2006 Nico Gauger and Andreas Griewank3rd European Workshop on Automatic Differentiation
FastOptADFLOWer by TAF( )
Test configuration2d NACA0012k-omega (Wilcox) turbulence modelcell-centred metric2000 time steps on fine gridtarget sensitivity: d lift/ d alpha
can be bounded away from zero. Then one can design a line
search procedure for determining such that the iterates
βα , H
kγ
Automated extension of fixed-point PDE solversfor optimal design with bounded retardation
(Griewank)
Slide 24
Oxford, June 1st, 2006 Nico Gauger and Andreas Griewank3rd European Workshop on Automatic Differentiation
Goals:Full fidelity optimization without model reductionAutomated adjoint generation with verifiable resultsBounded retardation of the original convergence rate Bounded increase of computational effort per stepBounded increase in overall storage requirementEfficient storage and linear algebra for the preconditioner of the combined iterationSelective evaluation or approximation of second derivativesStability with respect to the design parameterization
Automated extension of fixed-point PDE solversfor optimal design with bounded retardation