document: Electromagnetics computations using the MPI parallel implementation of the steepest descent fast multipole method -LRB- SDFMM -RRB- 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 -LRB- message passing interface -RRB- parallel implementation of the steepest descent fast multipole method -LRB- SDFMM -RRB- . 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 -LRB- 1 -RRB- filling the sparse impedance matrix associated with the near-field method of moments interactions -LRB- MoM -RRB- , -LRB- 2 -RRB- the matrix vector multiplications associated with this sparse matrix and -LRB- 3 -RRB- 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
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