A More Scalable and Efficient Parallelization of the Adaptive Integral Method—Part II: BIOEM Application

Abstract

The parallelization of the adaptive integral method proposed in Part I is used to solve 3-D scattering problems pertinent to bioelectromagnetic (BIOEM) analysis. Detailed numerical results are presented to quantify the computational complexity and parallel efficiency of the method on a petascale supercomputing cluster. Boundaries of acceptable parallelization regions of the method are identified in the plane under realistic resource and efficiency constraints, where and denote the number of unknowns and processes, respectively. These regions are shown to be larger than those of an alternative parallelization method for benchmark BIOEM problems. The proposed method is also used to compute the power absorbed by an anatomical human body model to demonstrate its potential for solving complex BIOEM problems. The computations are performed for increasingly higher resolutions of the model and the power absorbed by the entire model and specific tissues in it are compared to safety standards. The highest resolution body model leads to an extreme problem with about 1.2 billion unknowns; the absolute parallel efficiency of the power-absorption simulation with this model is shown to be approximately 78% for matrix fill operations, 66% for memory requirement, and 30% for iterative solution on 8192 processes.Index Terms-Bioelectromagnetics, fast Fourier transform (FFT), integral equations, parallel algorithms, parallel efficiency, visible human project.

Parallel PWTD-Accelerated Explicit Solution of the Time-Domain Electric Field Volume Integral Equation

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Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS)

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