A Preconditioned GMRES Method for Solving a Sideways Parabolic Equation in Two Space Dimensions
2010 (English)Report (Other academic)
The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a non-characteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed: the solution does not depend continuously on the data. We consider both one and two-dimensional SPE with both constant and variable coefficients. We apply the preconditioned Generalized Minimum Residuals Method (GMRES) on these problems. Preconditioners are chosen in ways that allow efficient implementation using the Fast Fourier Transform (FFT). Regularization is used in the preconditioner as well as truncating the GMRES algorithm. Numerical experiments demonstrate that the proposed method works well.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2010. , 36 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2010:3
Cauchy problem, inverse problem, ill-posed, iterative methods, GMRES preconditioning, FFT, parabolic PDE
IdentifiersURN: urn:nbn:se:liu:diva-54298OAI: oai:DiVA.org:liu-54298DiVA: diva2:302601