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Abstract:
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A hybrid of message passing and shared memory techniques is presented for scalable parallelization of the adaptive integral method (AIM ) , an FFT based algorithm , on clusters of identical multi -core processors . The proposed hybrid MPI /OpenMP parallelization scheme is based on a nested one -dimensional (1 -D ) slab decomposition of the 3 -D auxiliary uniform grid and the associated AIM calculations : If there are M processors and T cores per processor , the scheme (i ) divides the uniform grid into M slabs and MT sub -slabs , (ii ) assigns each slab /sub -slab and the associated operations to one of the processors /cores , and (iii ) uses MPI for inter -processor data communication and OpenMP for intra -processor data exchange . The MPI /OpenMP parallel AIM is used to accelerate the MOM solution of combined -field integral equations pertinent to the analysis of scattering from perfectly conducting surfaces . The scalability and efficiency of the implementation are investigated theoretically and verified numerically by solving benchmark scattering problems on a (near ) petaflop supercomputing cluster of quad -core processors . The timing and speedup results on up to 1024 processors show that the proposed hybrid MPI /OpenMP parallelization exhibits better strong scalability (fixed problem size speedup ) compared to pure MPI parallelization when multiple cores are used on each processor . |