An optimal iterative algorithm to solve Cauchy problem for Laplace equation

Handle URI:
http://hdl.handle.net/10754/576980
Title:
An optimal iterative algorithm to solve Cauchy problem for Laplace equation
Authors:
Majeed, Muhammad Usman ( 0000-0001-6296-2158 ) ; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
Abstract:
An optimal mean square error minimizer algorithm is developed to solve severely ill-posed Cauchy problem for Laplace equation on an annulus domain. The mathematical problem is presented as a first order state space-like system and an optimal iterative algorithm is developed that minimizes the mean square error in states. Finite difference discretization schemes are used to discretize first order system. After numerical discretization algorithm equations are derived taking inspiration from Kalman filter however using one of the space variables as a time-like variable. Given Dirichlet and Neumann boundary conditions are used on the Cauchy data boundary and fictitious points are introduced on the unknown solution boundary. The algorithm is run for a number of iterations using the solution of previous iteration as a guess for the next one. The method developed happens to be highly robust to noise in Cauchy data and numerically efficient results are illustrated.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
IEEE
Journal:
2015 3rd International Conference on Control, Engineering & Information Technology (CEIT)
Conference/Event name:
Control, Engineering & Information Technology (CEIT), 2015 3rd International Conference on
Issue Date:
25-May-2015
DOI:
10.1109/CEIT.2015.7233079
Type:
Conference Paper
Additional Links:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7233079
Appears in Collections:
Conference Papers; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorMajeed, Muhammad Usmanen
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.date.accessioned2015-09-09T05:41:02Zen
dc.date.available2015-09-09T05:41:02Zen
dc.date.issued2015-05-25en
dc.identifier.doi10.1109/CEIT.2015.7233079en
dc.identifier.urihttp://hdl.handle.net/10754/576980en
dc.description.abstractAn optimal mean square error minimizer algorithm is developed to solve severely ill-posed Cauchy problem for Laplace equation on an annulus domain. The mathematical problem is presented as a first order state space-like system and an optimal iterative algorithm is developed that minimizes the mean square error in states. Finite difference discretization schemes are used to discretize first order system. After numerical discretization algorithm equations are derived taking inspiration from Kalman filter however using one of the space variables as a time-like variable. Given Dirichlet and Neumann boundary conditions are used on the Cauchy data boundary and fictitious points are introduced on the unknown solution boundary. The algorithm is run for a number of iterations using the solution of previous iteration as a guess for the next one. The method developed happens to be highly robust to noise in Cauchy data and numerically efficient results are illustrated.en
dc.publisherIEEEen
dc.relation.urlhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7233079en
dc.titleAn optimal iterative algorithm to solve Cauchy problem for Laplace equationen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journal2015 3rd International Conference on Control, Engineering & Information Technology (CEIT)en
dc.conference.date25-27 May 2015en
dc.conference.nameControl, Engineering & Information Technology (CEIT), 2015 3rd International Conference onen
dc.conference.locationTlemcen, Algeriaen
dc.eprint.versionPublisher's Version/PDFen
kaust.authorMajeed, Muhammad Usmanen
kaust.authorLaleg-Kirati, Taous-Meriemen
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