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An Iterative Method for Problems with Multiscale Conductivity
Joint Authors
Je Woo, Eung
Kim, Hyea Hyun
Minhas, Atul S.
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-05
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
A model with its conductivity varying highly across a very thin layer will be considered.
It is related to a stable phantom model, which is invented to generate a certain apparent conductivity inside a region surrounded by a thin cylinder with holes.
The thin cylinder is an insulator and both inside and outside the thin cylinderare filled with the same saline.
The injected current can enter only through the holes adopted to the thin cylinder.
The model has a high contrast of conductivity discontinuity across the thin cylinder and the thickness of the layer and the size of holes are very small compared to the domain of the model problem.
Numerical methods for such a model require a very fine mesh near the thin layer to resolve the conductivity discontinuity.
In this work, an efficient numerical method for such a model problem is proposed by employing a uniform mesh, which need not resolve the conductivity discontinuity.
The discrete problem is then solved by an iterative method, where the solution is improved by solving a simple discrete problem with a uniform conductivity.
At each iteration, the right-hand side is updated by integrating the previous iterate over the thin cylinder.
This process results in a certain smoothing effect on microscopic structures and our discrete model can provide a more practical tool for simulating the apparent conductivity.
The convergence of the iterative method is analyzed regarding the contrast in the conductivity and the relative thickness of the layer.
In numerical experiments, solutions of our method are compared to reference solutions obtained from COMSOL, where very fine meshes are used to resolve the conductivity discontinuity in the model.
Errors of the voltage in L2 norm follow O(h) asymptotically and the current density matches quitewell those from the reference solution for a sufficiently small mesh size h.
The experimental results present a promising feature of our approach for simulating the apparent conductivity related to changes in microscopic cellular structures.
American Psychological Association (APA)
Kim, Hyea Hyun& Minhas, Atul S.& Je Woo, Eung. 2012. An Iterative Method for Problems with Multiscale Conductivity. Computational and Mathematical Methods in Medicine،Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-505976
Modern Language Association (MLA)
Kim, Hyea Hyun…[et al.]. An Iterative Method for Problems with Multiscale Conductivity. Computational and Mathematical Methods in Medicine No. 2012 (2012), pp.1-12.
https://search.emarefa.net/detail/BIM-505976
American Medical Association (AMA)
Kim, Hyea Hyun& Minhas, Atul S.& Je Woo, Eung. An Iterative Method for Problems with Multiscale Conductivity. Computational and Mathematical Methods in Medicine. 2012. Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-505976
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-505976