A message passing finite volume algorithm for Maxwell’s equations on parallel machines

A zonal approach to solving the Maxwell’s equations for generalized body conformal curvilinear grids on parallel computers is presented. The 3-D finite volume algorithm is explicit in nature and is especially suited for the message passing paradigm. It utilizes a four stage Runge-Kutta time integration method. Integration of the Maxwell’s equations is carried out on a dual grid wherein the electric and magnetic field quantities are evaluated on different grids. Each zone is placed on a separate processor and inter-processor communication is carried out using the Message Passing Library (MPL). The algorithm has been successfully tested on the SP-2 in solving scattering problems of electromagnetic waves from various targets. RCS results are presented for the problem of scattering from a perfectly conducting sphere and a perfectly conducting ogive. These results are in extremely good agreement with the exact solution and with results obtained with a standard finite difference time domain code. Qualitative results are also provided for scattering from metallic trapezoidal wing, and an aircraft engine. The formulation used in this case is for the scattered field and the Liao boundary condition is used at the outer non-reflecting boundary. The far zone transformation has also been implemented efficiently to evaluate the far zone scattering results.