Abstract
dc:description.abstractMathematical modeling of physical processes often leads to systems of differential and algebraic equations involving quantities of interest. A computer model created based on these equations can be numerically integrated to predict future states of the system and its evolution in time. This thesis investigates current methods in numerical time-stepping schemes, identifying a number of important features needed to speed up and increase the accuracy of the solutions. The focus is on developing new methods suitable for large-scale applications with multiple physical processes, potentially with significant differences in their time-scales. Various families of new methods are introduced with special attention to multirating, low computational cost implicitness, high order of convergence, and robustness. For each family, the order condition theory is discussed and a number of examples are derived. The accuracy and stability of the methods are investigated using standard analysis techniques and numerical experiments are performed to verify the abilities of the new methods.
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Computer Science and Applications
- Department dc:contributor.department
- Computer Science
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2021
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Sarshar, Arash
- Chair dc:contributor.committeechair
-
- Sandu, Adrian
- Committee members dc:contributor.committeemember
-
- Woodward, Carol S.
- Cao, Young
- Ribbens, Calvin J.
- Iliescu, Traian
Subjects
dc:subject × 2Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:32445
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/104969