Show simple item record

dc.contributor.authorTranquilli, Paul J.en_US
dc.date.accessioned2018-02-01T07:00:20Z
dc.date.available2018-02-01T07:00:20Z
dc.date.issued2016-08-09en_US
dc.identifier.othervt_gsexam:8623en_US
dc.identifier.urihttp://hdl.handle.net/10919/81974
dc.description.abstractMany scientific and engineering applications require the solution of large systems of initial value problems arising from method of lines discretization of partial differential equations. For systems with widely varying time scales, or with complex physical dynamics, implicit time integration schemes are preferred due to their superior stability properties. However, for very large systems accurate solution of the implicit terms can be impractical. For this reason approximations are widely used in the implementation of such methods. The primary focus of this work is on the development of novel ``lightly-implicit'' time integration methodologies. These methods consider the time integration and the solution of the implicit terms as a single computational process. We propose several classes of lightly-implicit methods that can be constructed to allow for different, specific approximations. Rosenbrock-Krylov and exponential-Krylov methods are designed to permit low accuracy Krylov based approximations of the implicit terms, while maintaining full order of convergence. These methods are matrix free, have low memory requirements, and are particularly well suited to parallel architectures. Linear stability analysis of K-methods is leveraged to construct implementation improvements for both Rosenbrock-Krylov and exponential-Krylov methods. Linearly-implicit Runge-Kutta-W methods are designed to permit arbitrary, time dependent, and stage varying approximations of the linear stiff dynamics of the initial value problem. The methods presented here are constructed with approximate matrix factorization in mind, though the framework is flexible and can be extended to many other approximations. The flexibility of lightly-implicit methods, and their ability to leverage computationally favorable approximations makes them an ideal alternative to standard explicit and implicit schemes for large parallel applications.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 Integrationen_US
dc.subjectNumerical PDEsen_US
dc.subjectNumerical ODEsen_US
dc.titleLightly-Implicit Methods for the Time Integration of Large Applicationsen_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.committeememberRibbens, Calvin J.en_US
dc.contributor.committeememberCao, Yangen_US
dc.contributor.committeememberDe Sturler, Ericen_US
dc.contributor.committeememberTokman, Mayyaen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record