Ahmed, Faysol (2015) Linearized domain decomposition approaches for boundary value problems. Masters thesis, Memorial University of Newfoundland.
- Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.
The purpose of this study is to analyze linearized domain decomposition approaches for different nonlinear boundary value problems (BVPs). Nonlinear BVPs frequently form a large system of equations when they are discretized and require parallel computers to solve this system. Domain decomposition approaches are useful to utilize the advantages of parallel computers in order to solve the differential equations. Cherpion’s single domain linearized iterative technique is quite useful to solve the nonlinear BVPs that have the form u′′ = f(ξ, u, u′ ). However with this iterative scheme we are not able to solve the BVP using parallel computers. Therefore we extend this iterative scheme to the domain decomposition context so that we can solve the nonlinear BVP on parallel computers. Theoretical and numerical results are given.
|Item Type:||Thesis (Masters)|
|Additional Information:||Includes bibliographical references (pages 178-180).|
|Keywords:||Linearized Domain Decomposition, Boundary Value Problems|
|Department(s):||Science, Faculty of > Computer Science|
|Library of Congress Subject Heading:||Nonlinear boundary value problems--Numerical solutions; Decomposition method; Differential equations, Partial|
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