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On the discrete adjoints of adaptive time stepping algorithms

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dc.contributor.authorAlexe, Mihaien
dc.contributor.authorSandu, Adrianen
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2013-06-19T14:36:15Zen
dc.date.available2013-06-19T14:36:15Zen
dc.date.issued2008-04-01en
dc.description.abstractWe investigate the behavior of adaptive time stepping numerical algorithms under the reverse mode of automatic differentiation (AD). By differentiating the time step controller and the error estimator of the original algorithm, reverse mode AD generates spurious adjoint derivatives of the time steps. The resulting discrete adjoint models become inconsistent with the adjoint ODE, and yield incorrect derivatives. To regain consistency, one has to cancel out the contributions of the non-physical derivatives in the discrete adjoint model. We demonstrate that the discrete adjoint models of one-step, explicit adaptive algorithms, such as the Runge--Kutta schemes, can be made consistent with their continuous analogs using simple code modifications. Furthermore, we extend the analysis to cover second order adjoint models derived through an extra forward-mode differentiation of the discrete adjoint code. Two numerical examples support the mathematical derivations.en
dc.format.mimetypeapplication/pdfen
dc.identifierhttp://eprints.cs.vt.edu/archive/00001028/en
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00001028/01/adaptive_adjoints_TR.pdfen
dc.identifier.trnumberTR-08-08en
dc.identifier.urihttp://hdl.handle.net/10919/19806en
dc.language.isoenen
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen
dc.relation.ispartofComputer Science Technical Reportsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMathematical softwareen
dc.titleOn the discrete adjoints of adaptive time stepping algorithmsen
dc.typeTechnical reporten
dc.type.dcmitypeTexten

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