A dimension decomposition approach based on iterative observer design for an elliptic Cauchy problem

Handle URI:
http://hdl.handle.net/10754/559953
Title:
A dimension decomposition approach based on iterative observer design for an elliptic Cauchy problem
Authors:
Majeed, Muhammad Usman ( 0000-0001-6296-2158 ) ; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
Abstract:
A state observer inspired iterative algorithm is presented to solve boundary estimation problem for Laplace equation using one of the space variables as a time-like variable. Three dimensional domain with two congruent parallel surfaces is considered. Problem is set up in cartesian co-ordinates and Laplace equation is re-written as a first order state equation with state operator matrix A and measurements are provided on the Cauchy data surface with measurement operator C. Conditions for the existence of strongly continuous semigroup generated by A are studied. Observability conditions for pair (C, A) are provided in infinite dimensional setting. In this given setting, special observability result obtained allows to decompose three dimensional problem into a set of independent two dimensional sub-problems over rectangular cross-sections. Numerical simulation results are provided.
KAUST Department:
Applied Mathematics and Computational Science Program
Issue Date:
13-Jul-2015
Type:
Article
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorMajeed, Muhammad Usmanen
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.date.accessioned2015-07-13T12:33:49Zen
dc.date.available2015-07-13T12:33:49Zen
dc.date.issued2015-07-13en
dc.identifier.urihttp://hdl.handle.net/10754/559953en
dc.description.abstractA state observer inspired iterative algorithm is presented to solve boundary estimation problem for Laplace equation using one of the space variables as a time-like variable. Three dimensional domain with two congruent parallel surfaces is considered. Problem is set up in cartesian co-ordinates and Laplace equation is re-written as a first order state equation with state operator matrix A and measurements are provided on the Cauchy data surface with measurement operator C. Conditions for the existence of strongly continuous semigroup generated by A are studied. Observability conditions for pair (C, A) are provided in infinite dimensional setting. In this given setting, special observability result obtained allows to decompose three dimensional problem into a set of independent two dimensional sub-problems over rectangular cross-sections. Numerical simulation results are provided.en
dc.language.isoenen
dc.subjectBoundary Estimationen
dc.subjectObserversen
dc.subjectelliptic equationen
dc.subjectinfinite dimensional systemsen
dc.titleA dimension decomposition approach based on iterative observer design for an elliptic Cauchy problemen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.eprint.versionPre-printen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
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