Solving the steadystate heat equation using overdetermined nonoverlapping domain decomposition methods
(2018) In Master's Theses in Mathematical Sciences FMN820 20172Mathematics (Faculty of Engineering)
 Abstract
 Domain decomposition methods can be used to numerically solve partial differential equations for certain problems, for example in cases where the domain has an irregular shape, or if there are differences in material constants. By splitting the domain into subdomains, these problems can be solved using domain decomposition methods. In this thesis, the topic is solving the steadystate heat equation using more than one boundary condition for each subdomain, causing the domain decomposition method to be overdetermined. The least squares method is used to handle this, and so it is explored if, by modifying the method to use parts of the mathematical formulation as constraints, the method will find an adequate approximation to the steadystate... (More)
 Domain decomposition methods can be used to numerically solve partial differential equations for certain problems, for example in cases where the domain has an irregular shape, or if there are differences in material constants. By splitting the domain into subdomains, these problems can be solved using domain decomposition methods. In this thesis, the topic is solving the steadystate heat equation using more than one boundary condition for each subdomain, causing the domain decomposition method to be overdetermined. The least squares method is used to handle this, and so it is explored if, by modifying the method to use parts of the mathematical formulation as constraints, the method will find an adequate approximation to the steadystate heat equation. It was found that overdetermined domain decomposition methods can indeed find a good approximation of the temperature distribution, and that using a constrained least squares method with different types of relaxation, can decrease the number of iterations to reach termination. This paves way for more work in relation to the use of overdetermined domain decomposition methods. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8946627
 author
 Thor, Filip ^{LU}
 supervisor

 Claus Führer ^{LU}
 Philipp Birken ^{LU}
 organization
 course
 FMN820 20172
 year
 2018
 type
 H2  Master's Degree (Two Years)
 subject
 keywords
 Overdetermined nonoverlapping domain decomposition methods, constrained least squares methods, steadystate heat equation
 publication/series
 Master's Theses in Mathematical Sciences
 report number
 LUFTNA30432018
 ISSN
 14046342
 other publication id
 2018:E22
 language
 English
 id
 8946627
 date added to LUP
 20180611 15:53:37
 date last changed
 20180611 15:53:37
@misc{8946627, abstract = {Domain decomposition methods can be used to numerically solve partial differential equations for certain problems, for example in cases where the domain has an irregular shape, or if there are differences in material constants. By splitting the domain into subdomains, these problems can be solved using domain decomposition methods. In this thesis, the topic is solving the steadystate heat equation using more than one boundary condition for each subdomain, causing the domain decomposition method to be overdetermined. The least squares method is used to handle this, and so it is explored if, by modifying the method to use parts of the mathematical formulation as constraints, the method will find an adequate approximation to the steadystate heat equation. It was found that overdetermined domain decomposition methods can indeed find a good approximation of the temperature distribution, and that using a constrained least squares method with different types of relaxation, can decrease the number of iterations to reach termination. This paves way for more work in relation to the use of overdetermined domain decomposition methods.}, author = {Thor, Filip}, issn = {14046342}, keyword = {Overdetermined nonoverlapping domain decomposition methods,constrained least squares methods,steadystate heat equation}, language = {eng}, note = {Student Paper}, series = {Master's Theses in Mathematical Sciences}, title = {Solving the steadystate heat equation using overdetermined nonoverlapping domain decomposition methods}, year = {2018}, }