On efficient solutions to the continuous sensitivity equation using automatic differentiation

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dc.contributor.authorBorggaard, Jeffrey T.en
dc.contributor.authorVerma, Arunen
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:08Zen
dc.date.available2014-05-28T18:35:08Zen
dc.date.issued2000-06en
dc.description.abstractShape sensitivity analysis is a tool that provides quantitative information about the influence of shape parameter changes on the solution of a partial differential equation (PDE). These shape sensitivities are described by a continuous sensitivity equation (CSE). Automatic differentiation (AD) can be used to perform this sensitivity analysis without writing any additional code to solve the sensitivity equation. The approximate solution of the PDE uses a spatial discretization (mesh) that often depends on the shape parameters. Therefore, the straightforward application of AD introduces derivatives of the mesh. There are two drawbacks to this approach. First, extra computational effort (especially memory) is used in these calculations due to mesh sensitivities. Second, this mesh sensitivity information needs to be computed in order to obtain accurate results. In this work, we provide a methodology that avoids mesh sensitivities (and their drawbacks) by defining a modified PDE on a fixed domain (i.e., independent of the shape parameter) such that AD provides the desired approximation of the CSE. Using two examples, we demonstrate significant improvement in the computational effort, both in terms of floating point operations and memory requirements. We explain how these code modifications can be applied to a wide variety of practical problems with minimal changes to the original code. These changes are negligible when compared to the complexity of writing a separate solver for the sensitivity equation.en
dc.format.mimetypeapplication/pdfen
dc.identifier.citationBorggaard, J.; Verma, A., "On efficient solutions to the continuous sensitivity equation using automatic differentiation," SIAM J. Sci. Comput., 22(1), 39-62, (2000). DOI: 10.1137/s1064827599352136en
dc.identifier.doihttps://doi.org/10.1137/s1064827599352136en
dc.identifier.issn1064-8275en
dc.identifier.urihttp://hdl.handle.net/10919/48156en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/S1064827599352136en
dc.language.isoen_USen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectsmall shape optimizationen
dc.subjectautomatic differentiationen
dc.subjectcontinuousen
dc.subjectsensitivity equationen
dc.subjectshape sensitivityen
dc.subjectmesh sensitivityen
dc.subjectboundaryen
dc.subjectconditionsen
dc.subjectadmaten
dc.subjectadmiten
dc.subjectmathematics, applieden
dc.titleOn efficient solutions to the continuous sensitivity equation using automatic differentiationen
dc.title.serialSiam Journal on Scientific Computingen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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