A 2-D decomposition based parallelization of AIM for 3-D BIOEM problems

A novel parallelization of the adaptive integral method (AIM) is presented for accelerating the large-scale solution of volume integral equations pertinent to bioelectromagnetics (BIOEM) problems. The proposed method improves the parallel scalability of AIM by (i) using different workload distribution strategies to load balance the different steps of the algorithm (rather than a single global decomposition strategy) and (ii) using a 2-D rather than a 1-D stencil decomposition of the auxiliary grid to parallelize the 3-D FFTs and the related anterpolation/interpolation steps. With the proposed modifications, the maximum number of processes that can be used effectively scales as P
^max
∼ N
^2/3
, where N denotes the number of volumetric unknowns. Numerical results demonstrate the scalability of the method and its application to BIOEM problems.