Iterative solution methods
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
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In this work, we consider large-scale finite element modeling on voxel grids. We are targeting the IBM Blue Gene/P computer, which features a 3D torus interconnect. Our previous parallelization approach was to divide the domain in one spatial direction only, which lead to limited parallelism. Here, we extend it to all three spatial directions in order to match the interconnect topology. As a sample problem, we consider the simulation of the thermal and electrical processes, involved in the radio-frequency (RF) ablation procedure. RF ablation is a low invasive technique for the treatment of hepatic tumors, utilizing AC current to destroy the tumor cells by heating. A 3D voxel approach is used for finite element method (FEM) approximation of the involved partial differential equations. After the space discretization, the backward Euler scheme is used for the time stepping. We study the impact of the domain partitioning on the performance of a parallel preconditioned conjugate gradient (PCG) solver for the arising large linear systems. As a preconditioner, we use BoomerAMG --- a parallel algebraic multigrid implementation from the package Hypre, developed in LLNL, Livermore. The implementation is tested on the IBM Blue Gene/P massively parallel computer.