On the Solution of Linear Equations
(2012) In Historielärarnas Förenings Årsskrift- Abstract
- n this paper a constrained system of linear equations is considered. These equations do, for instance, appear as a result of finite element formulations of static equilibrium problem for solids. Two classical methods for the solution of the equations are discussed; the method using elimination of constrained coordinates and a method using Lagrangian multipliers. The relation to the minimization of the mechanical energy is elucidated. Existence of solutions is proved under specific conditions and the methods are compared in some examples. It is also shown that the method using elimination of constrained coordinates can be simplified considerably if periodic boundary conditions are introduced in the equilibrium problem.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2296625
- author
- Ahadi, Aylin LU and Lidström, Per LU
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- unpublished
- subject
- keywords
- constraints, linear equations, Lagrangean multipliers
- in
- Historielärarnas Förenings Årsskrift
- publisher
- Historielärarnas förening
- ISSN
- 0439-2434
- language
- English
- LU publication?
- yes
- id
- b74cb3ee-c605-4e9e-a5ee-0de5cae92f27 (old id 2296625)
- date added to LUP
- 2016-04-04 14:38:14
- date last changed
- 2019-11-25 09:04:14
@article{b74cb3ee-c605-4e9e-a5ee-0de5cae92f27, abstract = {{n this paper a constrained system of linear equations is considered. These equations do, for instance, appear as a result of finite element formulations of static equilibrium problem for solids. Two classical methods for the solution of the equations are discussed; the method using elimination of constrained coordinates and a method using Lagrangian multipliers. The relation to the minimization of the mechanical energy is elucidated. Existence of solutions is proved under specific conditions and the methods are compared in some examples. It is also shown that the method using elimination of constrained coordinates can be simplified considerably if periodic boundary conditions are introduced in the equilibrium problem.}}, author = {{Ahadi, Aylin and Lidström, Per}}, issn = {{0439-2434}}, keywords = {{constraints; linear equations; Lagrangean multipliers}}, language = {{eng}}, publisher = {{Historielärarnas förening}}, series = {{Historielärarnas Förenings Årsskrift}}, title = {{On the Solution of Linear Equations}}, year = {{2012}}, }