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In this paper, we analyze the communication pattern and study the scalability of a distributed memory implementation of the multilevel fast multipole algorithm (MLFMA) called ScaleME. ScaleME uses the message passing interface (MPI) for communication between processors. The parallelization of MLFMA uses a novel a hybrid scheme for distributing the workload across the processors. We study the communication and computational behavior and demonstrate the effectiveness of the parallelization scheme using realistic problems.

The fast inhomogeneous plane wave algorithm has been developed to accelerate the solution of three-dimensional electromagnetic scattering problems in free space. By expanding the kernel of the Green's function using the Weyl identity and choosing a proper steepest descent path, the diagonalization of the translation matrix is achieved after the interpolation and extrapolation techniques are applied. The proposed algorithm is implemented on top of the scalable multipole engine, a portable implementation of the dynamic multilevel fast multipole algorithm for distributed-memory computers. The computational time per matrix vector multiplication is reduced to O(NlogN) and the memory requirement is reduced to O(N), where N is the number of unknowns in the discretized integral equation. The algorithm is validated by applying it to the solution of the electromagnetic scattering from the perfect electric conducting scatterers. This approach can be easily extended to more general problems with complicated Green's function expressed in terms of the plane wave spectral integrals, such as the ones encountered in the multilayered medium studies.

A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme.

In this paper, we have presented the major features and some preliminary results from the parallel fast multipole library, ScaleME (scalable multipole engine). We have briefly outlined the major features of the library and its applications.

In this paper, we present a higher-order multilevel fast multipole algorithm (MLFMA) for solving integral equations of electromagnetic wave scattering by three-dimensional conducting objects. We first employ higher-order parametric elements to provide an accurate modeling of the scatterer's geometry and then higher-order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. The resultant numerical system of equations is then solved using the MLFMA with a reduced computational complexity. Appropriate preconditioning techniques are employed to speedup the MLFMA solution.