A Preconditioned GMRES Method for Solving a 1D Sideways Heat Equation
2010 (English)Report (Other academic)
The sideways Heat equation (SHE) 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 use a preconditioned Generalized Minimum Residuals Method (GMRES) to solve a 1D SHE. 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 University Electronic Press , 2010. , 16 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2010:6
Cauchy problem, ill-posed, iterative methods, GMRES, heat equation
IdentifiersURN: urn:nbn:se:liu:diva-61152OAI: oai:DiVA.org:liu-61152DiVA: diva2:360739