Iterative solution methods
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
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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We consider large scale finite element modeling on 3D unstructured grids. Large scale problems imply the use of parallel hardware and software. In general, the computational process on unstructured grids includes: mesh generation, mesh partitioning, optional mesh refinement, discretization, and the solution. The impact of the domain partitioning strategy on the performance of the discretization and solution stages is studied. Our investigations are focused on the Blue Gene/P massively parallel computer. The mapping of the communications to the underlying 3D tours interconnect topology is considered as well. 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.