Denserks: Fortran Sensitivity Solvers Using Continuous, Explicit Runge-kutta Schemes

dc.contributor.authorAlexe, Mihaien
dc.contributor.authorSandu, Adrianen
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2013-06-19T14:36:47Zen
dc.date.available2013-06-19T14:36:47Zen
dc.date.issued2007-10-01en
dc.description.abstractDENSERKS is a Fortran sensitivity equation solver package designed for integrating models whose evolution can be described by ordinary differential equations (ODEs). A salient feature of DENSERKS is its support for both forward and adjoint sensitivity analyses, with built-in integrators for both first and second order continuous adjoint models. The software implements explicit Runge-Kutta methods with adaptive timestepping and high-order dense output schemes for the forward and the tangent linear model trajectory interpolation. Implementations of six Runge-Kutta methods are provided, with orders of accuracy ranging from two to eight. This makes DENSERKS suitable for a wide range of practical applications. The use of dense output, a novel approach in adjoint sensitivity analysis solvers, allows for a high-order cost-effective interpolation. This is a necessary feature when solving adjoints of nonlinear systems using highly accurate Runge-Kutta methods (order five and above). To minimize memory requirements and make long-time integrations computationally efficient, DENSERKS implements a two-level checkpointing mechanism. The code is tested on a selection of problems illustrating first and second order sensitivity analysis with respect to initial model conditions. The resulting derivative information is also used in a gradient-based optimization algorithm to minimize cost functionals dependent on a given set of model parameters.en
dc.format.mimetypeapplication/pdfen
dc.identifierhttp://eprints.cs.vt.edu/archive/00000996/en
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000996/01/denserks.pdfen
dc.identifier.trnumberTR-07-34en
dc.identifier.urihttp://hdl.handle.net/10919/19843en
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.titleDenserks: Fortran Sensitivity Solvers Using Continuous, Explicit Runge-kutta Schemesen
dc.typeTechnical reporten
dc.type.dcmitypeTexten

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