Newton method for estimation of the Robin coefficient

Volume 8, Issue 5, pp 660--669 http://dx.doi.org/10.22436/jnsa.008.05.18

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Authors

Yan-Bo Ma - Department of Mathematics and Statist, Hanshan Normal University, Chaozhou, Guangdong, 521041, P. R. China.

Abstract

This paper considers estimation of Robin parameter by using measurements on partial boundary and solving a Robin inverse problem associated with the Laplace equation. Typically, such problems are solved utilizing a Gauss-Newton method in which the forward model constraints are implicitly incorporated. Variants of Newton’s method which use second derivative information are rarely employed because their perceived disadvantage in computational cost per step offsets their potential benefits of fast convergence. In this paper, we show that by formulating the inversion as a constrained or unconstrained optimization problem, we can carry out the sequential quadratic programming and the full Newton iteration with only a modest additional cost. Our numerical results illustrate that Newton’s method can produce a solution in fewer iterations and, in some cases where the data contain significant noise, requires fewer floating point operations than Gauss- Newton methods.

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Keywords

• Robin inverse problem
• ill-posedness
• boundary integral equations
• Newton method
• Gauss-Newton method.

MSC

•  45Q05
•  65N21

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