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RESISTOR NETWORKS AND FINITE ELEMENT MODELS

Al Humaidi, Abdulaziz

[Thesis]. Manchester, UK: The University of Manchester; 2011.

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Abstract

There are two commonly discrete approximations for the inverse conductivity problem.Finite element models are heavily used in electrical impedance tomography research as they are easily adapted to bodies of irregular shapes. The other approximation is to use electrical resistor networks for which several uniqueness results and reconstruction algorithms are known for the inverse problem. In this thesis the link between finite element models and resistor networks is established. For the planar case we show how resistor networks associated with a triangular mesh have an isotropic embedding and we give conditions for the uniqueness of the embedding. Moreover, a layered finite element model parameterized by thevalues of conductivity on the interior nodes is constructed. Construction of the finite element mesh leads to a study of the triangulation survey problem. A constructive algorithm is given to determine the position of the nodes in the triangulation with a knowledge of one edge and the angles of the finite element mesh. Also we show that we need to satisfy the sine rule as aconsistency condition for every closed basic cycle that enclosing interior nodes and this is a complete set of independent constraints.

Bibliographic metadata

Type of resource:
Content type:
Form of thesis:
Type of submission:
Degree type:
Doctor of Philosophy
Degree programme:
PhD Mathematical Sciences
Publication date:
Location:
Manchester, UK
Total pages:
156
Abstract:
There are two commonly discrete approximations for the inverse conductivity problem.Finite element models are heavily used in electrical impedance tomography research as they are easily adapted to bodies of irregular shapes. The other approximation is to use electrical resistor networks for which several uniqueness results and reconstruction algorithms are known for the inverse problem. In this thesis the link between finite element models and resistor networks is established. For the planar case we show how resistor networks associated with a triangular mesh have an isotropic embedding and we give conditions for the uniqueness of the embedding. Moreover, a layered finite element model parameterized by thevalues of conductivity on the interior nodes is constructed. Construction of the finite element mesh leads to a study of the triangulation survey problem. A constructive algorithm is given to determine the position of the nodes in the triangulation with a knowledge of one edge and the angles of the finite element mesh. Also we show that we need to satisfy the sine rule as aconsistency condition for every closed basic cycle that enclosing interior nodes and this is a complete set of independent constraints.
Thesis main supervisor(s):
Thesis advisor(s):
Language:
en

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:125388
Created by:
Al Humaidi, Abdulaziz
Created:
27th June, 2011, 09:13:39
Last modified by:
Al Humaidi, Abdulaziz
Last modified:
5th July, 2011, 14:11:17

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