Linearized domain decomposition approaches for boundary value problems

Ahmed, Faysol (2015) Linearized domain decomposition approaches for boundary value problems. Masters thesis, Memorial University of Newfoundland.

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Abstract

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.

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