Regularization of the noisy Cauchy problem solution approximated by an energy-like method

SUMMARYThis paper focuses on the regularization of noisy Cauchy data and unknown boundary conditions approximated by the energy‐like minimization method. After providing considerations necessary for the numerical analysis leading to an adequate stopping criterion for the minimization process, we des...

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Veröffentlicht in:	International journal for numerical methods in engineering 2013-07, Vol.95 (4), p.271-287
Hauptverfasser:	Rischette, R., Baranger, T. N., Andrieux, S.
Format:	Artikel
Sprache:	eng
Schlagworte:	Acoustic signal processing Acoustics Approximation boundary conditions identification Cauchy problem Computer Science data completion denoising Engineering Sciences Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematical models Mathematics Mechanics Minimization noisy Cauchy problem Numerical analysis Optimization Optimization and Control Ordinary differential equations Partial differential equations Physics Regularization Reproduction Sciences and techniques of general use Signal and Image processing Solid mechanics stopping criterion Thermics
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Zusammenfassung:	SUMMARYThis paper focuses on the regularization of noisy Cauchy data and unknown boundary conditions approximated by the energy‐like minimization method. After providing considerations necessary for the numerical analysis leading to an adequate stopping criterion for the minimization process, we describe the denoising procedure proposed. Numerical experiments involving singular data are presented.Copyright © 2013 John Wiley & Sons, Ltd.
ISSN:	0029-5981 1097-0207
DOI:	10.1002/nme.4501