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dc.contributor.authorZhang, Hongen_US
dc.date.accessioned2014-09-10T08:00:11Z
dc.date.available2014-09-10T08:00:11Z
dc.date.issued2014-09-09en_US
dc.identifier.othervt_gsexam:3646en_US
dc.identifier.urihttp://hdl.handle.net/10919/50492
dc.description.abstractMany fields in science and engineering require large-scale numerical simulations of complex systems described by differential equations. These systems are typically multi-physics (they are driven by multiple interacting physical processes) and multiscale (the dynamics takes place on vastly different spatial and temporal scales). Numerical solution of such systems is highly challenging due to the dimension of the resulting discrete problem, and to the complexity that comes from incorporating multiple interacting components with different characteristics. The main contributions of this dissertation are the creation of new families of time integration methods for multiscale and multiphysics simulations, and the development of industrial-strengh tools for sensitivity analysis. This work develops novel implicit-explicit (IMEX) general linear time integration methods for multiphysics and multiscale simulations typically involving both stiff and non-stiff components. In an IMEX approach, one uses an implicit scheme for the stiff components and an explicit scheme for the non-stiff components such that the combined method has the desired stability and accuracy properties. Practical schemes with favorable properties, such as maximized stability, high efficiency, and no order reduction, are constructed and applied in extensive numerical experiments to validate the theoretical findings and to demonstrate their advantages. Approximate matrix factorization (AMF) technique exploits the structure of the Jacobian of the implicit parts, which may lead to further efficiency improvement of IMEX schemes. We have explored the application of AMF within some high order IMEX Runge-Kutta schemes in order to achieve high efficiency. Sensitivity analysis gives quantitative information about the changes in a dynamical model outputs caused by caused by small changes in the model inputs. This information is crucial for data assimilation, model-constrained optimization, inverse problems, and uncertainty quantification. We develop a high performance software package for sensitivity analysis in the context of stiff and nonstiff ordinary differential equations. Efficiency is demonstrated by direct comparisons against existing state-of-art software on a variety of test problems.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectTime Steppingen_US
dc.subjectGeneral Linear Methodsen_US
dc.subjectImplicit-expliciten_US
dc.subjectSensitivity Analysisen_US
dc.titleEfficient Time Stepping Methods and Sensitivity Analysis for Large Scale Systems of Differential Equationsen_US
dc.typeDissertationen_US
dc.contributor.departmentComputer Scienceen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineComputer Science and Applicationsen_US
dc.contributor.committeechairSandu, Adrianen_US
dc.contributor.committeememberCao, Yangen_US
dc.contributor.committeememberSpiteri, Raymond Johnen_US
dc.contributor.committeememberLin, Taoen_US
dc.contributor.committeememberRibbens, Calvin J.en_US
dc.contributor.committeememberIliescu, Traianen_US


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