TY - GEN

T1 - An optimal iterative algorithm to solve Cauchy problem for Laplace equation

AU - Majeed, Muhammad Usman

AU - Laleg-Kirati, Taous-Meriem

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/9/3

Y1 - 2015/9/3

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/576980

UR - http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7233079

UR - http://www.scopus.com/inward/record.url?scp=84960172780&partnerID=8YFLogxK

U2 - 10.1109/CEIT.2015.7233079

DO - 10.1109/CEIT.2015.7233079

M3 - Conference contribution

SN - 9781479982127

BT - 2015 3rd International Conference on Control, Engineering & Information Technology (CEIT)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -