The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface
We investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. The algorithms considered are based on th...
Saved in:
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/787198 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562987516297216 |
|---|---|
| author | B. Sheehan D. Estep S. Tavener J. Cary S. Kruger A. Hakim A. Pletzer J. Carlsson S. Vadlamani |
| author_facet | B. Sheehan D. Estep S. Tavener J. Cary S. Kruger A. Hakim A. Pletzer J. Carlsson S. Vadlamani |
| author_sort | B. Sheehan |
| collection | DOAJ |
| description | We investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. The algorithms considered are based on the widely used approach of iteratively exchanging boundary condition data on the shared boundary at each time step. There exists a significant and sophisticated numerical analysis of such methods. However, computations for practical applications are often carried out under conditions under which it is unclear if rigorous results apply while relatively few iterations are used per time step. To examine this situation, we derive exact matrix expressions for the propagation of the error due to incomplete iteration that can be readily evaluated for specific discretization parameters. Using the formulas, we show that the universal validity of several tenants of the practitioner’s conventional wisdom are not universally valid. |
| format | Article |
| id | doaj-art-f4e1198c6e8d40c5ba82d94902d77063 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-f4e1198c6e8d40c5ba82d94902d770632025-02-03T01:21:27ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/787198787198The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an InterfaceB. Sheehan0D. Estep1S. Tavener2J. Cary3S. Kruger4A. Hakim5A. Pletzer6J. Carlsson7S. Vadlamani8Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USADepartment of Statistics, Colorado State University, Fort Collins, CO 80523, USADepartment of Mathematics, Colorado State University, Fort Collins, CO 80523, USATech X Corporation, Boulder, CO 80303, USATech X Corporation, Boulder, CO 80303, USATech X Corporation, Boulder, CO 80303, USATech X Corporation, Boulder, CO 80303, USATech X Corporation, Boulder, CO 80303, USATech X Corporation, Boulder, CO 80303, USAWe investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. The algorithms considered are based on the widely used approach of iteratively exchanging boundary condition data on the shared boundary at each time step. There exists a significant and sophisticated numerical analysis of such methods. However, computations for practical applications are often carried out under conditions under which it is unclear if rigorous results apply while relatively few iterations are used per time step. To examine this situation, we derive exact matrix expressions for the propagation of the error due to incomplete iteration that can be readily evaluated for specific discretization parameters. Using the formulas, we show that the universal validity of several tenants of the practitioner’s conventional wisdom are not universally valid.http://dx.doi.org/10.1155/2015/787198 |
| spellingShingle | B. Sheehan D. Estep S. Tavener J. Cary S. Kruger A. Hakim A. Pletzer J. Carlsson S. Vadlamani The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface Advances in Mathematical Physics |
| title | The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface |
| title_full | The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface |
| title_fullStr | The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface |
| title_full_unstemmed | The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface |
| title_short | The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface |
| title_sort | interaction of iteration error and stability for linear partial differential equations coupled through an interface |
| url | http://dx.doi.org/10.1155/2015/787198 |
| work_keys_str_mv | AT bsheehan theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT destep theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT stavener theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT jcary theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT skruger theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT ahakim theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT apletzer theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT jcarlsson theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT svadlamani theinteractionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT bsheehan interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT destep interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT stavener interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT jcary interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT skruger interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT ahakim interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT apletzer interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT jcarlsson interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface AT svadlamani interactionofiterationerrorandstabilityforlinearpartialdifferentialequationscoupledthroughaninterface |