Parallel algorithms for adaptive time-stepping in radiofrequency liver ablation simulation: implementation on an IBM Blue Gene/P computer

This work concerns the mathematical modeling and computer simulations of the heat transfer process. The core is solving the time-dependent partial differential equation of parabolic type. Instead of a uniform discretization of the considered time interval, an adaptive time-stepping procedure is applied in an effort to decrease the simulation time. The procedure is based on the local comparison of the Crank Nicholson and backward Euler approximations. Computer simulation on geometry obtained from a magnetic resonance imaging (MRI) scan of the patient is performed. Results of some preliminary numerical experiments performed on a selected test problems are presented and discussed