430	RWTH Publication No: 481391        2015        IGPM430.pdf
TITLE	Certified Reduced Order Methods for Optimal Treatment Planning
AUTHORS	Bahodir Ahmedov, Martin A. Grepl, Michael Herty
ABSTRACT	We study numerical methods for inverse problems arising in cancer therapy treatment under uncertainty. The interest is on efficient and reliable numerical methods that allow to determine the influence of possible unknown parameters on the treatment plan for cancer therapy. The Boltzmann transport equation is used to model the evolution of charged particles in tissue. A mixed variational framework is presented and existence and uniqueness of a weak solution is established. The optimality system is approximated using a low–dimensional reduced basis formulation based on a PN-FE discretization. We derive a posteriori bounds for the error in the reduced basis solution of the optimal control problem with respect to the solution of the PN-FE discretization. Numerical results in slab geometry are presented to confirm the validity of our approach.
KEYWORDS	optimal radiotherapy, reduced basis methods, a posteriori error estimation, PN - methods, mixed variational formulation
DOI	10.1142/S0218202516500159
PUBLICATION	Mathematical Models and Methods in Applied Sciences 26(4), 2016, pp. 699-727