Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation

Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are needed to take advantage of the increasing computational resources and utilize the emerging hardware and software infrastructure with maximum efficiency. Adaptive numerical discretization methods can accommodate problems with various physical, scale, and dynamic features by adjusting the resolution, order, and the type of method used to solve them. In applications that simulate real systems, the numerical accuracy of the solution is typically just one of the challenges. Measurements can be included in the simulation to constrain the numerical solution through a process called data assimilation in order to anchor the simulation in reality. In this thesis we investigate adaptive discretization methods and data assimilation approaches for large-scale numerical simulations. We develop and investigate novel multirate and implicit-explicit methods that are appropriate for multiscale and multiphysics numerical discretizations. We construct and explore data assimilation approaches for, but not restricted to, atmospheric chemistry applications. A generic approach for describing the structure of the uncertainty in initial conditions that can be applied to the most popular data assimilation approaches is also presented. We show that adaptive numerical methods can effectively address the discretization of large-scale problems. Data assimilation complements the adaptive numerical methods by correcting the numerical solution with real measurements. Test problems and large-scale numerical experiments validate the theoretical findings. Synergistic approaches that use adaptive numerical methods within a data assimilation framework need to be investigated in the future.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Computer Science

Department dc:contributor.department

Computer Science

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2008

Author dc:creator

• Constantinescu, Emil Mihai

Chair dc:contributor.committeechair

• Sandu, Adrian

Committee members dc:contributor.committeemember

• Iliescu, Traian
• Ryan, Jennifer K.
• Santos, Eunice E.
• Ribbens, Calvin J.
• Watson, Layne T.

• data assimilation
• IMEX
• multirate
• ODE and PDE time integration

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-06032008-095855

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/27938