Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method
2014 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 30, no 1, 015005- p.Article in journal (Refereed) Published
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.
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
IdentifiersURN: urn:nbn:se:liu:diva-103280DOI: 10.1088/0266-5611/30/1/015005ISI: 000328861800006OAI: oai:DiVA.org:liu-103280DiVA: diva2:688509