Supercomputer Simulation of Radio‐frequency Hepatic Tumor Ablation

We simulate the thermal and electrical processes, involved in the radio‐frequency (RF) ablation procedure. The mathematical model consists of two parts—electrical and thermal. The energy from the applied AC voltage is determined first, by solving the Laplace equation to find the potential distribution. After that, the electric field intensity and the current density are directly calculated. Finally, the heat transfer equation is solved to determine the temperature distribution. Heat loss due to blood perfusion is also accounted for.The representation of the computational domain is based on a voxel mesh. Both partial differential equations are discretized in space via linear conforming FEM. After the space discretization, the backward Euler scheme is used for the time stepping.Large‐scale linear systems arise from the FEM discretization. Moreover, they are ill‐conditioned, due to the strong coefficient jumps and the complex geometry of the problem. Therefore, efficient parallel solution methods are required.The developed parallel solver is based on the preconditioned conjugate gradient (PCG) method. As a preconditioner, we use BoomerAMG—a parallel algebraic multigrid implementation from the package Hypre, developed in LLNL, Livermore.Parallel numerical tests, performed on the IBM Blue Gene/P massively parallel computer are presented.We simulate the thermal and electrical processes, involved in the radio‐frequency (RF) ablation procedure. The mathematical model consists of two parts—electrical and thermal. The energy from the applied AC voltage is determined first, by solving the Laplace equation to find the potential distribution. After that, the electric field intensity and the current density are directly calculated. Finally, the heat transfer equation is solved to determine the temperature distribution. Heat loss due to blood perfusion is also accounted for.The representation of the computational domain is based on a voxel mesh. Both partial differential equations are discretized in space via linear conforming FEM. After the space discretization, the backward Euler scheme is used for the time stepping.Large‐scale linear systems arise from the FEM discretization. Moreover, they are ill‐conditioned, due to the strong coefficient jumps and the complex geometry of the problem. Therefore, efficient parallel solution methods are require...