A More Scalable and Efficient Parallelization of the Adaptive Integral Method—Part I: Algorithm

A more effective parallelization of the adaptive integral method (AIM) is proposed for solving the 3-D volume electric field integral equation. The AIM computations are distributed among processes by employing two workload decomposition strategies: 1) a novel 2-D pencil decomposition of the auxiliary regular grid is used to parallelize the anterpolation, interpolation, and 3-D FFT-accelerated propagation steps; and 2) a balanced 3-D block decomposition of the scattering volume is used to parallelize the correction step. The scalability of the proposed parallelization method is investigated theoretically. To compare it with competing methods, the concepts of resource constraints, parallel efficiency constraints, scalability limits, and acceptable parallelization regions are introduced by using N-P plots, where N and P denote the number of unknowns and processes, respectively. Using these concepts, it is shown that the proposed parallelization of AIM has better weak and strong scalability compared to the traditional ones, i.e., it enables not only larger problems to be solved but also faster solution of a given problem by increasing P.

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