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Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method
Xidian University, Xi'an, China .
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
2014 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 30, no 1, 015005- p.Article in journal (Refereed) Published
Abstract [en]

An ill-posed Cauchy problem for a 3D elliptic partial differential equation with variable coefficients is considered. A well-posed quasi-boundary-value (QBV) problem is given to approximate it. Some stability estimates are given. For the numerical implementation, a large sparse system is obtained from discretizing the QBV problem using the finite difference method. A left-preconditioned generalized minimum residual method is used to solve the large system effectively. For the preconditioned system, a fast solver using the fast Fourier transform is given. Numerical results show that the method works well.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2014. Vol. 30, no 1, 015005- p.
Keyword [en]
elliptic equation; ill-posed; Cauchy problem; finite difference method; quasi-boundary-value method; left-preconditioned GMRES; fast solver; variable coefficients; three dimensions; fast Fourier transform
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-103280DOI: 10.1088/0266-5611/30/1/015005ISI: 000328861800006OAI: oai:DiVA.org:liu-103280DiVA: diva2:688509
Available from: 2014-01-17 Created: 2014-01-16 Last updated: 2017-12-06Bibliographically approved

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Eldén, Lars
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