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Preconditioning of One‐Shot Pseudo‐Timestepping Methods for Shape Optimization
Author(s) -
Gherman Ilia,
Schulz Volker
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510345
Subject(s) - ode , ordinary differential equation , shot (pellet) , computer science , optimal design , state (computer science) , mathematical optimization , one shot , mathematics , differential equation , algorithm , mathematical analysis , mechanical engineering , engineering , materials science , machine learning , metallurgy
One‐shot pseudo‐timestepping [1, 2] has proven to be a powerful approach for the solution of optimal design problems in engineering applications. It blends well in within pre‐existing pseudo‐timestepping simulation solvers. The goal of this approach is to transform the equations for the necessary optimality conditions of the optimal design problem into an ordinary differential equation (ODE) and then solve the pseudo‐time embedded state, co‐state and design equations all at once. Similar approaches have been considered in [4, 5]. An application of this method to a real‐world example within the MEGADESIGN‐Project has been presented in [3]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)