In this talk will be presented an adaptive finite element method for solution of a linear Fredholm integral equation of the first kind.
A posteriori error estimates in the functional to be minimized, and in the regularized solution to
this functional, will be derived and corresponding adaptive finite element algorithms will be formulated.
Balancing principle for optimal choice of the regularization parameter will be also discussed.
Finally, numerical experiments will show the efficiency of a
an adaptive finite element method applied to data measured in microwave
thermometry. The data is provided by a group of Biomedical
Imaging (M. Aram, H. Dobsicek-Trefna) at the Department of Electrical
Engineering at Chalmers, Gothenburg, Sweden, which works on the development of systems for
hyperthermia treatment of deep-seated cancerous tumors using microwave
M. G. Aram, L. Beilina, H. Dobsicek Trefna, Microwave Thermometry with Potential Application in Non-invasive Monitoring of Hyperthermia, Journal of Inverse and Ill-posed problems,
2020, DOI: https://doi.org/10.1515/jiip-2020-0102