TY - JOUR

T1 - On efficient reconstruction of boundary data with optimal placement of the source points in the MFS: application to inverse Stefan problems

T2 - application to inverse Stefan problems

AU - Vynnycky, Michael

AU - Reddy, G. M.M.

AU - Cuminato, J. A.

N1 - Publisher Copyright:
© 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2018/9/2

Y1 - 2018/9/2

N2 - Current practice in the use of the method of fundamental solutions (MFS) for inverse Stefan problems typically involves setting the source and collocation points at some distance, h, from the boundaries of the domain in which the solution is required, and then varying their number, N, so that the obtained solution fulfils a desired tolerance, Tol, when a random noise level δ is added to the boundary conditions. This leads to an open question: can h and N be chosen simultaneously so that N is minimized, thereby leading to a lower computational expense in the solution of the inverse problem? Here, we develop a novel, simple and practical algorithm to help answer this question. The algorithm is used to study the effect of Tol and δ on both h and N. Its effectiveness is shown through three test problems and numerical experiments show promising results: for example, even with δ as high as 5% and Tol as low as 10-3, we are able to find satisfactory solutions for N as low as 8.

AB - Current practice in the use of the method of fundamental solutions (MFS) for inverse Stefan problems typically involves setting the source and collocation points at some distance, h, from the boundaries of the domain in which the solution is required, and then varying their number, N, so that the obtained solution fulfils a desired tolerance, Tol, when a random noise level δ is added to the boundary conditions. This leads to an open question: can h and N be chosen simultaneously so that N is minimized, thereby leading to a lower computational expense in the solution of the inverse problem? Here, we develop a novel, simple and practical algorithm to help answer this question. The algorithm is used to study the effect of Tol and δ on both h and N. Its effectiveness is shown through three test problems and numerical experiments show promising results: for example, even with δ as high as 5% and Tol as low as 10-3, we are able to find satisfactory solutions for N as low as 8.

KW - 65K10

KW - 65N35

KW - algorithm

KW - Inverse Stefan problem

KW - method of fundamental solutions

KW - noise

KW - source points

UR - http://www.scopus.com/inward/record.url?scp=85032383483&partnerID=8YFLogxK

U2 - 10.1080/17415977.2017.1391244

DO - 10.1080/17415977.2017.1391244

M3 - Article

AN - SCOPUS:85032383483

SN - 1741-5977

VL - 26

SP - 1249

EP - 1279

JO - Inverse Problems in Science and Engineering

JF - Inverse Problems in Science and Engineering

IS - 9

ER -