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Numerical simulation for the shape reconstruction of a cavity
Author(s) -
Yan WenJing,
Ma YiChen
Publication year - 2009
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20356
Subject(s) - mathematics , partial derivative , inverse problem , boundary (topology) , domain (mathematical analysis) , partial differential equation , differential operator , operator (biology) , nonlinear system , boundary value problem , mathematical analysis , derivative (finance) , numerical analysis , inverse , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , financial economics , economics , gene
We consider the inverse problem of reconstructing the interior boundary curve of a cavity from the knowledge of the measurements on the exterior boundary. The domain derivative of the corresponding operator is presented, and this allows the investigation of the regularized Newton method for the solution of the ill‐posed and nonlinear problem. Numerical examples indicate the feasibility of our method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009