title: Electromagnetics computations using the MPI parallel implementation of the steepest descent fast multipole method (SDFMM)
abstract: The computational solution of large-scale linear systems of equations necessitates the use of fast algorithms but is also greatly enhanced by employing parallelization techniques. The objective of this work is to demonstrate the speedup achieved by the MPI (message passing interface) parallel implementation of the steepest descent fast multipole method (SDFMM). Although this algorithm has already been optimized to take advantage of the structure of the physics of scattering problems, there is still the opportunity to speed up the calculation by dividing tasks into components using multiple processors and solve them in parallel. The SDFMM has three bottlenecks ordered as (1) filling the sparse impedance matrix associated with the near-field method of moments interactions (MoM), (2) the matrix vector multiplications associated with this sparse matrix and (3) the far field interactions associated with the fast multipole method. The parallel implementation task is accomplished using a thirty-one node Intel Pentium Beowulf cluster and is also validated on a 4-processor Alpha workstation. The Beowulf cluster consists of thirty-one nodes of 350 MHz Intel Pentium IIs with 256 MB of RAM and one node of a 4*450 MHz Intel Pentium II Xeon shared memory processor with 2 GB of RAM with all nodes connected to a 100 BaseTX Ethernet network. The Alpha workstation has a maximum of four 667 MHz processors. Our numerical results show significant linear speedup in filling the sparse impedance matrix. Using the 32-processors on the Beowulf cluster lead to a 7.2 overall speedup while a 2.5 overall speedup is gained using the 4-processors on the Alpha workstation
keyphrases: electromagnetics computations MPI parallel implementation steepest descent fast multipole method large-scale linear systems fast algorithms message passing interface physics scattering problems multiple processors sparse impedance matrix method of moments matrix vector multiplications Intel Pentium Beowulf cluster 4-processor Alpha workstation 350 MHz Intel Pentium II RAM 450 MHz Xeon shared memory processor 100 BaseTX Ethernet network 667 MHz near-field MoM scattered electric field scattered magnetic field 256 MByte 2 GByte